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+\relax
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@@ -0,0 +1,25 @@
+% Appendix A
+
+\chapter{Frequently Asked Questions} % Main appendix title
+
+\label{AppendixA} % For referencing this appendix elsewhere, use \ref{AppendixA}
+
+\section{How do I change the colors of links?}
+
+The color of links can be changed to your liking using:
+
+{\small\verb!\hypersetup{urlcolor=red}!}, or
+
+{\small\verb!\hypersetup{citecolor=green}!}, or
+
+{\small\verb!\hypersetup{allcolor=blue}!}.
+
+\noindent If you want to completely hide the links, you can use:
+
+{\small\verb!\hypersetup{allcolors=.}!}, or even better:
+
+{\small\verb!\hypersetup{hidelinks}!}.
+
+\noindent If you want to have obvious links in the PDF but not the printed text, use:
+
+{\small\verb!\hypersetup{colorlinks=false}!}.
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/Appendices/AppendixTemplate.tex Sun Mar 20 23:32:08 2022 +0000
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+% Appendix Template
+
+\chapter{Appendix Title Here} % Main appendix title
+
+\label{AppendixX} % Change X to a consecutive letter; for referencing this appendix elsewhere, use \ref{AppendixX}
+
+Write your Appendix content here.
\ No newline at end of file
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+\@writefile{toc}{\contentsline {subsection}{\numberline {1.8.1}Printing Format}{8}{subsection.28}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {1.8.2}Using US Letter Paper}{9}{subsection.29}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {1.8.3}References}{9}{subsection.30}}
+\@writefile{toc}{\contentsline {subsubsection}{A Note on bibtex}{9}{section*.32}}
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+\@writefile{toc}{\contentsline {section}{\numberline {1.10}In Closing}{12}{section.40}}
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+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/Chapters/Chapter1.tex Sun Mar 20 23:32:08 2022 +0000
@@ -0,0 +1,730 @@
+% Chapter 1
+
+\chapter{Introduction} % Main chapter title
+
+\label{Chapter1} % For referencing the chapter elsewhere, use \ref{Chapter1}
+
+%----------------------------------------------------------------------------------------
+
+% Define some commands to keep the formatting separated from the content
+\newcommand{\keyword}[1]{\textbf{#1}}
+\newcommand{\tabhead}[1]{\textbf{#1}}
+\newcommand{\code}[1]{\texttt{#1}}
+\newcommand{\file}[1]{\texttt{\bfseries#1}}
+\newcommand{\option}[1]{\texttt{\itshape#1}}
+
+
+\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}%
+\newcommand{\ZERO}{\mbox{\bf 0}}
+\newcommand{\ONE}{\mbox{\bf 1}}
+\def\lexer{\mathit{lexer}}
+\def\mkeps{\mathit{mkeps}}
+
+\def\DFA{\textit{DFA}}
+\def\bmkeps{\textit{bmkeps}}
+\def\retrieve{\textit{retrieve}}
+\def\blexer{\textit{blexer}}
+\def\flex{\textit{flex}}
+\def\inj{\mathit{inj}}
+\def\Empty{\mathit{Empty}}
+\def\Left{\mathit{Left}}
+\def\Right{\mathit{Right}}
+\def\Stars{\mathit{Stars}}
+\def\Char{\mathit{Char}}
+\def\Seq{\mathit{Seq}}
+\def\Der{\mathit{Der}}
+\def\nullable{\mathit{nullable}}
+\def\Z{\mathit{Z}}
+\def\S{\mathit{S}}
+\def\rup{r^\uparrow}
+\def\simp{\mathit{simp}}
+\def\simpALTs{\mathit{simp}\_\mathit{ALTs}}
+\def\map{\mathit{map}}
+\def\distinct{\mathit{distinct}}
+\def\blexersimp{\mathit{blexer}\_\mathit{simp}}
+%----------------------------------------------------------------------------------------
+
+
+
+
+Regular expression matching and lexing has been
+ widely-used and well-implemented
+in software industry.
+If you go to a popular programming language's
+regex engine,
+you can supply it with regex and strings of your own,
+and get matching/lexing information such as how a
+sub-part of the regex matches a sub-part of the string.
+These lexing libraries are on average quite fast.
+For example, the regex engines some network intrusion detection
+systems use are able to process
+ megabytes or even gigabytes of network traffic per second.
+
+Why do we need to have our version, if the algorithms work well on
+average?
+
+
+Take $(a^*)^*\,b$ and ask whether
+strings of the form $aa..a$ match this regular
+expression. Obviously this is not the case---the expected $b$ in the last
+position is missing. One would expect that modern regular expression
+matching engines can find this out very quickly. Alas, if one tries
+this example in JavaScript, Python or Java 8 with strings like 28
+$a$'s, one discovers that this decision takes around 30 seconds and
+takes considerably longer when adding a few more $a$'s, as the graphs
+below show:
+
+\begin{center}
+\begin{tabular}{@{}c@{\hspace{0mm}}c@{\hspace{0mm}}c@{}}
+\begin{tikzpicture}
+\begin{axis}[
+ xlabel={$n$},
+ x label style={at={(1.05,-0.05)}},
+ ylabel={time in secs},
+ enlargelimits=false,
+ xtick={0,5,...,30},
+ xmax=33,
+ ymax=35,
+ ytick={0,5,...,30},
+ scaled ticks=false,
+ axis lines=left,
+ width=5cm,
+ height=4cm,
+ legend entries={JavaScript},
+ legend pos=north west,
+ legend cell align=left]
+\addplot[red,mark=*, mark options={fill=white}] table {re-js.data};
+\end{axis}
+\end{tikzpicture}
+ &
+\begin{tikzpicture}
+\begin{axis}[
+ xlabel={$n$},
+ x label style={at={(1.05,-0.05)}},
+ %ylabel={time in secs},
+ enlargelimits=false,
+ xtick={0,5,...,30},
+ xmax=33,
+ ymax=35,
+ ytick={0,5,...,30},
+ scaled ticks=false,
+ axis lines=left,
+ width=5cm,
+ height=4cm,
+ legend entries={Python},
+ legend pos=north west,
+ legend cell align=left]
+\addplot[blue,mark=*, mark options={fill=white}] table {re-python2.data};
+\end{axis}
+\end{tikzpicture}
+ &
+\begin{tikzpicture}
+\begin{axis}[
+ xlabel={$n$},
+ x label style={at={(1.05,-0.05)}},
+ %ylabel={time in secs},
+ enlargelimits=false,
+ xtick={0,5,...,30},
+ xmax=33,
+ ymax=35,
+ ytick={0,5,...,30},
+ scaled ticks=false,
+ axis lines=left,
+ width=5cm,
+ height=4cm,
+ legend entries={Java 8},
+ legend pos=north west,
+ legend cell align=left]
+\addplot[cyan,mark=*, mark options={fill=white}] table {re-java.data};
+\end{axis}
+\end{tikzpicture}\\
+\multicolumn{3}{c}{Graphs: Runtime for matching $(a^*)^*\,b$ with strings
+ of the form $\underbrace{aa..a}_{n}$.}
+\end{tabular}
+\end{center}
+
+
+This is clearly exponential behaviour, and
+is triggered by some relatively simple regex patterns.
+
+
+
+The opens up the possibility of
+ a ReDoS (regular expression denial-of-service ) attack.
+
+Theoretical results say that regular expression matching
+should be linear with respect to the input. You could construct
+an NFA via Thompson construction, and simulate running it.
+This would be linear.
+Or you could determinize the NFA into a DFA, and minimize that
+DFA. Once you have the DFA, the running time is also linear, requiring just
+one scanning pass of the input.
+
+But modern regex libraries in popular language engines
+ often want to support richer constructs
+than the most basic regular expressions such as bounded repetitions
+and back references.
+%put in illustrations
+%a{1}{3}
+These make a DFA construction impossible because
+of an exponential states explosion.
+ They also want to support lexing rather than just matching
+ for tasks that involves text processing.
+
+ Existing regex libraries either pose restrictions on the user input, or does
+ not give linear running time guarantee.
+ %TODO: give examples such as RE2 GOLANG 1000 restriction, rust no repetitions
+ For example, the Rust regex engine claims to be linear,
+ but does not support lookarounds and back-references.
+ The GoLang regex library does not support over 1000 repetitions.
+ Java and Python both support back-references, but shows
+catastrophic backtracking behaviours on inputs without back-references(
+when the language is still regular).
+ %TODO: test performance of Rust on (((((a*a*)b*)b){20})*)c baabaabababaabaaaaaaaaababaaaababababaaaabaaabaaaaaabaabaabababaababaaaaaaaaababaaaababababaaaaaaaaaaaaac
+ %TODO: verify the fact Rust does not allow 1000+ reps
+ %TODO: Java 17 updated graphs? Is it ok to still use Java 8 graphs?
+ Another thing about the these libraries is that there
+ is no correctness guarantee.
+ In some cases they either fails to generate a lexing result when there is a match,
+ or gives the wrong way of matching.
+
+
+This superlinear blowup in matching algorithms sometimes causes
+considerable grief in real life: for example on 20 July 2016 one evil
+regular expression brought the webpage
+\href{http://stackexchange.com}{Stack Exchange} to its
+%knees.\footnote{\url{https://stackstatus.net/post/147710624694/outage-postmortem-july-20-2016}}
+In this instance, a regular expression intended to just trim white
+spaces from the beginning and the end of a line actually consumed
+massive amounts of CPU-resources---causing web servers to grind to a
+halt. This happened when a post with 20,000 white spaces was submitted,
+but importantly the white spaces were neither at the beginning nor at
+the end. As a result, the regular expression matching engine needed to
+backtrack over many choices. In this example, the time needed to process
+the string was $O(n^2)$ with respect to the string length. This
+quadratic overhead was enough for the homepage of Stack Exchange to
+respond so slowly that the load balancer assumed there must be some
+attack and therefore stopped the servers from responding to any
+requests. This made the whole site become unavailable. Another very
+recent example is a global outage of all Cloudflare servers on 2 July
+2019. A poorly written regular expression exhibited exponential
+behaviour and exhausted CPUs that serve HTTP traffic. Although the
+outage had several causes, at the heart was a regular expression that
+was used to monitor network
+%traffic.\footnote{\url{https://blog.cloudflare.com/details-of-the-cloudflare-outage-on-july-2-2019/}}
+
+ Is it possible to have a regex lexing algorithm with proven correctness and
+ time complexity, which allows easy extensions to
+ constructs like
+ bounded repetitions, negation, lookarounds, and even back-references?
+
+ We propose Brzozowski's derivatives as a solution to this problem.
+
+
+ \section{Why Brzozowski}
+ In the last fifteen or so years, Brzozowski's derivatives of regular
+expressions have sparked quite a bit of interest in the functional
+programming and theorem prover communities.
+The beauty of
+Brzozowski's derivatives \parencite{Brzozowski1964} is that they are neatly
+expressible in any functional language, and easily definable and
+reasoned about in theorem provers---the definitions just consist of
+inductive datatypes and simple recursive functions.
+
+Suppose we have an alphabet $\Sigma$, the strings whose characters
+are from $\Sigma$
+can be expressed as $\Sigma^*$.
+
+We use patterns to define a set of strings concisely. Regular expressions
+are one of such patterns systems:
+The basic regular expressions are defined inductively
+ by the following grammar:
+\[ r ::= \ZERO \mid \ONE
+ \mid c
+ \mid r_1 \cdot r_2
+ \mid r_1 + r_2
+ \mid r^*
+\]
+
+The language or set of strings defined by regular expressions are defined as
+%TODO: FILL in the other defs
+\begin{center}
+\begin{tabular}{lcl}
+$L \; r_1 + r_2$ & $\dn$ & $ L \; r_1 \cup L \; r_2$\\
+$L \; r_1 \cdot r_2$ & $\dn$ & $ L \; r_1 \cap L \; r_2$\\
+\end{tabular}
+\end{center}
+Which are also called the "language interpretation".
+
+
+
+The Brzozowski derivative w.r.t character $c$ is an operation on the regex,
+where the operation transforms the regex to a new one containing
+strings without the head character $c$.
+
+Formally, we define first such a transformation on any string set, which
+we call semantic derivative:
+\begin{center}
+$\Der \; c\; \textit{StringSet} = \{s \mid c :: s \in StringSet\}$
+\end{center}
+Mathematically, it can be expressed as the
+
+If the $\textit{StringSet}$ happen to have some structure, for example,
+if it is regular, then we have that it
+
+The the derivative of regular expression, denoted as
+$r \backslash c$, is a function that takes parameters
+$r$ and $c$, and returns another regular expression $r'$,
+which is computed by the following recursive function:
+
+\begin{center}
+\begin{tabular}{lcl}
+ $\ZERO \backslash c$ & $\dn$ & $\ZERO$\\
+ $\ONE \backslash c$ & $\dn$ & $\ZERO$\\
+ $d \backslash c$ & $\dn$ &
+ $\mathit{if} \;c = d\;\mathit{then}\;\ONE\;\mathit{else}\;\ZERO$\\
+$(r_1 + r_2)\backslash c$ & $\dn$ & $r_1 \backslash c \,+\, r_2 \backslash c$\\
+$(r_1 \cdot r_2)\backslash c$ & $\dn$ & $\mathit{if} \, nullable(r_1)$\\
+ & & $\mathit{then}\;(r_1\backslash c) \cdot r_2 \,+\, r_2\backslash c$\\
+ & & $\mathit{else}\;(r_1\backslash c) \cdot r_2$\\
+ $(r^*)\backslash c$ & $\dn$ & $(r\backslash c) \cdot r^*$\\
+\end{tabular}
+\end{center}
+\noindent
+\noindent
+
+The $\nullable$ function tests whether the empty string $""$
+is in the language of $r$:
+
+
+\begin{center}
+ \begin{tabular}{lcl}
+ $\nullable(\ZERO)$ & $\dn$ & $\mathit{false}$ \\
+ $\nullable(\ONE)$ & $\dn$ & $\mathit{true}$ \\
+ $\nullable(c)$ & $\dn$ & $\mathit{false}$ \\
+ $\nullable(r_1 + r_2)$ & $\dn$ & $\nullable(r_1) \vee \nullable(r_2)$ \\
+ $\nullable(r_1\cdot r_2)$ & $\dn$ & $\nullable(r_1) \wedge \nullable(r_2)$ \\
+ $\nullable(r^*)$ & $\dn$ & $\mathit{true}$ \\
+ \end{tabular}
+\end{center}
+\noindent
+The empty set does not contain any string and
+therefore not the empty string, the empty string
+regular expression contains the empty string
+by definition, the character regular expression
+is the singleton that contains character only,
+and therefore does not contain the empty string,
+the alternative regular expression(or "or" expression)
+might have one of its children regular expressions
+being nullable and any one of its children being nullable
+would suffice. The sequence regular expression
+would require both children to have the empty string
+to compose an empty string and the Kleene star
+operation naturally introduced the empty string.
+
+We can give the meaning of regular expressions derivatives
+by language interpretation:
+
+
+
+
+
+Derivatives give a simple solution
+to the problem of matching a string $s$ with a regular
+expression $r$: if the derivative of $r$ w.r.t.\ (in
+succession) all the characters of the string matches the empty string,
+then $r$ matches $s$ (and {\em vice versa}).
+
+
+
+However, there are two difficulties with derivative-based matchers:
+First, Brzozowski's original matcher only generates a yes/no answer
+for whether a regular expression matches a string or not. This is too
+little information in the context of lexing where separate tokens must
+be identified and also classified (for example as keywords
+or identifiers). Sulzmann and Lu~\cite{Sulzmann2014} overcome this
+difficulty by cleverly extending Brzozowski's matching
+algorithm. Their extended version generates additional information on
+\emph{how} a regular expression matches a string following the POSIX
+rules for regular expression matching. They achieve this by adding a
+second ``phase'' to Brzozowski's algorithm involving an injection
+function. In our own earlier work we provided the formal
+specification of what POSIX matching means and proved in Isabelle/HOL
+the correctness
+of Sulzmann and Lu's extended algorithm accordingly
+\cite{AusafDyckhoffUrban2016}.
+
+The second difficulty is that Brzozowski's derivatives can
+grow to arbitrarily big sizes. For example if we start with the
+regular expression $(a+aa)^*$ and take
+successive derivatives according to the character $a$, we end up with
+a sequence of ever-growing derivatives like
+
+\def\ll{\stackrel{\_\backslash{} a}{\longrightarrow}}
+\begin{center}
+\begin{tabular}{rll}
+$(a + aa)^*$ & $\ll$ & $(\ONE + \ONE{}a) \cdot (a + aa)^*$\\
+& $\ll$ & $(\ZERO + \ZERO{}a + \ONE) \cdot (a + aa)^* \;+\; (\ONE + \ONE{}a) \cdot (a + aa)^*$\\
+& $\ll$ & $(\ZERO + \ZERO{}a + \ZERO) \cdot (a + aa)^* + (\ONE + \ONE{}a) \cdot (a + aa)^* \;+\; $\\
+& & $\qquad(\ZERO + \ZERO{}a + \ONE) \cdot (a + aa)^* + (\ONE + \ONE{}a) \cdot (a + aa)^*$\\
+& $\ll$ & \ldots \hspace{15mm}(regular expressions of sizes 98, 169, 283, 468, 767, \ldots)
+\end{tabular}
+\end{center}
+
+\noindent where after around 35 steps we run out of memory on a
+typical computer (we shall define shortly the precise details of our
+regular expressions and the derivative operation). Clearly, the
+notation involving $\ZERO$s and $\ONE$s already suggests
+simplification rules that can be applied to regular regular
+expressions, for example $\ZERO{}\,r \Rightarrow \ZERO$, $\ONE{}\,r
+\Rightarrow r$, $\ZERO{} + r \Rightarrow r$ and $r + r \Rightarrow
+r$. While such simple-minded simplifications have been proved in our
+earlier work to preserve the correctness of Sulzmann and Lu's
+algorithm \cite{AusafDyckhoffUrban2016}, they unfortunately do
+\emph{not} help with limiting the growth of the derivatives shown
+above: the growth is slowed, but the derivatives can still grow rather
+quickly beyond any finite bound.
+
+
+Sulzmann and Lu overcome this ``growth problem'' in a second algorithm
+\cite{Sulzmann2014} where they introduce bitcoded
+regular expressions. In this version, POSIX values are
+represented as bitsequences and such sequences are incrementally generated
+when derivatives are calculated. The compact representation
+of bitsequences and regular expressions allows them to define a more
+``aggressive'' simplification method that keeps the size of the
+derivatives finite no matter what the length of the string is.
+They make some informal claims about the correctness and linear behaviour
+of this version, but do not provide any supporting proof arguments, not
+even ``pencil-and-paper'' arguments. They write about their bitcoded
+\emph{incremental parsing method} (that is the algorithm to be formalised
+in this paper):
+
+
+\begin{quote}\it
+ ``Correctness Claim: We further claim that the incremental parsing
+ method [..] in combination with the simplification steps [..]
+ yields POSIX parse trees. We have tested this claim
+ extensively [..] but yet
+ have to work out all proof details.'' \cite[Page 14]{Sulzmann2014}
+\end{quote}
+
+
+
+
+\section{Backgound}
+%Regular expression matching and lexing has been
+% widely-used and well-implemented
+%in software industry.
+%TODO: expand the above into a full paragraph
+%TODO: look up snort rules to use here--give readers idea of what regexes look like
+
+
+Theoretical results say that regular expression matching
+should be linear with respect to the input.
+Under a certain class of regular expressions and inputs though,
+practical implementations suffer from non-linear or even
+exponential running time,
+allowing a ReDoS (regular expression denial-of-service ) attack.
+
+
+%----------------------------------------------------------------------------------------
+
+\section{Existing Practical Approaches}
+
+The reason behind is that regex libraries in popular language engines
+ often want to support richer constructs
+than the most basic regular expressions, and lexing rather than matching
+is needed for sub-match extraction.
+
+
+
+\subsection{DFA Approach}
+
+Exponential states.
+
+\subsection{NFA Approach}
+Backtracking.
+
+
+
+%----------------------------------------------------------------------------------------
+
+\section{Our Approach}
+In the last fifteen or so years, Brzozowski's derivatives of regular
+expressions have sparked quite a bit of interest in the functional
+programming and theorem prover communities. The beauty of
+Brzozowski's derivatives \parencite{Brzozowski1964} is that they are neatly
+expressible in any functional language, and easily definable and
+reasoned about in theorem provers---the definitions just consist of
+inductive datatypes and simple recursive functions. Derivatives of a
+regular expression, written $r \backslash c$, give a simple solution
+to the problem of matching a string $s$ with a regular
+expression $r$: if the derivative of $r$ w.r.t.\ (in
+succession) all the characters of the string matches the empty string,
+then $r$ matches $s$ (and {\em vice versa}).
+
+
+This work aims to address the above vulnerability by the combination
+of Brzozowski's derivatives and interactive theorem proving. We give an
+improved version of Sulzmann and Lu's bit-coded algorithm using
+derivatives, which come with a formal guarantee in terms of correctness and
+running time as an Isabelle/HOL proof.
+Then we improve the algorithm with an even stronger version of
+simplification, and prove a time bound linear to input and
+cubic to regular expression size using a technique by
+Antimirov.
+
+\subsection{Existing Work}
+We are aware
+of a mechanised correctness proof of Brzozowski's derivative-based matcher in HOL4 by
+Owens and Slind~\parencite{Owens2008}. Another one in Isabelle/HOL is part
+of the work by Krauss and Nipkow \parencite{Krauss2011}. And another one
+in Coq is given by Coquand and Siles \parencite{Coquand2012}.
+Also Ribeiro and Du Bois give one in Agda \parencite{RibeiroAgda2017}.
+
+%----------------------------------------------------------------------------------------
+
+\section{What this Template Includes}
+
+\subsection{Folders}
+
+This template comes as a single zip file that expands out to several files and folders. The folder names are mostly self-explanatory:
+
+\keyword{Appendices} -- this is the folder where you put the appendices. Each appendix should go into its own separate \file{.tex} file. An example and template are included in the directory.
+
+\keyword{Chapters} -- this is the folder where you put the thesis chapters. A thesis usually has about six chapters, though there is no hard rule on this. Each chapter should go in its own separate \file{.tex} file and they can be split as:
+\begin{itemize}
+\item Chapter 1: Introduction to the thesis topic
+\item Chapter 2: Background information and theory
+\item Chapter 3: (Laboratory) experimental setup
+\item Chapter 4: Details of experiment 1
+\item Chapter 5: Details of experiment 2
+\item Chapter 6: Discussion of the experimental results
+\item Chapter 7: Conclusion and future directions
+\end{itemize}
+This chapter layout is specialised for the experimental sciences, your discipline may be different.
+
+\keyword{Figures} -- this folder contains all figures for the thesis. These are the final images that will go into the thesis document.
+
+\subsection{Files}
+
+Included are also several files, most of them are plain text and you can see their contents in a text editor. After initial compilation, you will see that more auxiliary files are created by \LaTeX{} or BibTeX and which you don't need to delete or worry about:
+
+\keyword{example.bib} -- this is an important file that contains all the bibliographic information and references that you will be citing in the thesis for use with BibTeX. You can write it manually, but there are reference manager programs available that will create and manage it for you. Bibliographies in \LaTeX{} are a large subject and you may need to read about BibTeX before starting with this. Many modern reference managers will allow you to export your references in BibTeX format which greatly eases the amount of work you have to do.
+
+\keyword{MastersDoctoralThesis.cls} -- this is an important file. It is the class file that tells \LaTeX{} how to format the thesis.
+
+\keyword{main.pdf} -- this is your beautifully typeset thesis (in the PDF file format) created by \LaTeX{}. It is supplied in the PDF with the template and after you compile the template you should get an identical version.
+
+\keyword{main.tex} -- this is an important file. This is the file that you tell \LaTeX{} to compile to produce your thesis as a PDF file. It contains the framework and constructs that tell \LaTeX{} how to layout the thesis. It is heavily commented so you can read exactly what each line of code does and why it is there. After you put your own information into the \emph{THESIS INFORMATION} block -- you have now started your thesis!
+
+Files that are \emph{not} included, but are created by \LaTeX{} as auxiliary files include:
+
+\keyword{main.aux} -- this is an auxiliary file generated by \LaTeX{}, if it is deleted \LaTeX{} simply regenerates it when you run the main \file{.tex} file.
+
+\keyword{main.bbl} -- this is an auxiliary file generated by BibTeX, if it is deleted, BibTeX simply regenerates it when you run the \file{main.aux} file. Whereas the \file{.bib} file contains all the references you have, this \file{.bbl} file contains the references you have actually cited in the thesis and is used to build the bibliography section of the thesis.
+
+\keyword{main.blg} -- this is an auxiliary file generated by BibTeX, if it is deleted BibTeX simply regenerates it when you run the main \file{.aux} file.
+
+\keyword{main.lof} -- this is an auxiliary file generated by \LaTeX{}, if it is deleted \LaTeX{} simply regenerates it when you run the main \file{.tex} file. It tells \LaTeX{} how to build the \emph{List of Figures} section.
+
+\keyword{main.log} -- this is an auxiliary file generated by \LaTeX{}, if it is deleted \LaTeX{} simply regenerates it when you run the main \file{.tex} file. It contains messages from \LaTeX{}, if you receive errors and warnings from \LaTeX{}, they will be in this \file{.log} file.
+
+\keyword{main.lot} -- this is an auxiliary file generated by \LaTeX{}, if it is deleted \LaTeX{} simply regenerates it when you run the main \file{.tex} file. It tells \LaTeX{} how to build the \emph{List of Tables} section.
+
+\keyword{main.out} -- this is an auxiliary file generated by \LaTeX{}, if it is deleted \LaTeX{} simply regenerates it when you run the main \file{.tex} file.
+
+So from this long list, only the files with the \file{.bib}, \file{.cls} and \file{.tex} extensions are the most important ones. The other auxiliary files can be ignored or deleted as \LaTeX{} and BibTeX will regenerate them.
+
+%----------------------------------------------------------------------------------------
+
+\section{Filling in Your Information in the \file{main.tex} File}\label{FillingFile}
+
+You will need to personalise the thesis template and make it your own by filling in your own information. This is done by editing the \file{main.tex} file in a text editor or your favourite LaTeX environment.
+
+Open the file and scroll down to the third large block titled \emph{THESIS INFORMATION} where you can see the entries for \emph{University Name}, \emph{Department Name}, etc \ldots
+
+Fill out the information about yourself, your group and institution. You can also insert web links, if you do, make sure you use the full URL, including the \code{http://} for this. If you don't want these to be linked, simply remove the \verb|\href{url}{name}| and only leave the name.
+
+When you have done this, save the file and recompile \code{main.tex}. All the information you filled in should now be in the PDF, complete with web links. You can now begin your thesis proper!
+
+%----------------------------------------------------------------------------------------
+
+\section{The \code{main.tex} File Explained}
+
+The \file{main.tex} file contains the structure of the thesis. There are plenty of written comments that explain what pages, sections and formatting the \LaTeX{} code is creating. Each major document element is divided into commented blocks with titles in all capitals to make it obvious what the following bit of code is doing. Initially there seems to be a lot of \LaTeX{} code, but this is all formatting, and it has all been taken care of so you don't have to do it.
+
+Begin by checking that your information on the title page is correct. For the thesis declaration, your institution may insist on something different than the text given. If this is the case, just replace what you see with what is required in the \emph{DECLARATION PAGE} block.
+
+Then comes a page which contains a funny quote. You can put your own, or quote your favourite scientist, author, person, and so on. Make sure to put the name of the person who you took the quote from.
+
+Following this is the abstract page which summarises your work in a condensed way and can almost be used as a standalone document to describe what you have done. The text you write will cause the heading to move up so don't worry about running out of space.
+
+Next come the acknowledgements. On this page, write about all the people who you wish to thank (not forgetting parents, partners and your advisor/supervisor).
+
+The contents pages, list of figures and tables are all taken care of for you and do not need to be manually created or edited. The next set of pages are more likely to be optional and can be deleted since they are for a more technical thesis: insert a list of abbreviations you have used in the thesis, then a list of the physical constants and numbers you refer to and finally, a list of mathematical symbols used in any formulae. Making the effort to fill these tables means the reader has a one-stop place to refer to instead of searching the internet and references to try and find out what you meant by certain abbreviations or symbols.
+
+The list of symbols is split into the Roman and Greek alphabets. Whereas the abbreviations and symbols ought to be listed in alphabetical order (and this is \emph{not} done automatically for you) the list of physical constants should be grouped into similar themes.
+
+The next page contains a one line dedication. Who will you dedicate your thesis to?
+
+Finally, there is the block where the chapters are included. Uncomment the lines (delete the \code{\%} character) as you write the chapters. Each chapter should be written in its own file and put into the \emph{Chapters} folder and named \file{Chapter1}, \file{Chapter2}, etc\ldots Similarly for the appendices, uncomment the lines as you need them. Each appendix should go into its own file and placed in the \emph{Appendices} folder.
+
+After the preamble, chapters and appendices finally comes the bibliography. The bibliography style (called \option{authoryear}) is used for the bibliography and is a fully featured style that will even include links to where the referenced paper can be found online. Do not underestimate how grateful your reader will be to find that a reference to a paper is just a click away. Of course, this relies on you putting the URL information into the BibTeX file in the first place.
+
+%----------------------------------------------------------------------------------------
+
+\section{Thesis Features and Conventions}\label{ThesisConventions}
+
+To get the best out of this template, there are a few conventions that you may want to follow.
+
+One of the most important (and most difficult) things to keep track of in such a long document as a thesis is consistency. Using certain conventions and ways of doing things (such as using a Todo list) makes the job easier. Of course, all of these are optional and you can adopt your own method.
+
+\subsection{Printing Format}
+
+This thesis template is designed for double sided printing (i.e. content on the front and back of pages) as most theses are printed and bound this way. Switching to one sided printing is as simple as uncommenting the \option{oneside} option of the \code{documentclass} command at the top of the \file{main.tex} file. You may then wish to adjust the margins to suit specifications from your institution.
+
+The headers for the pages contain the page number on the outer side (so it is easy to flick through to the page you want) and the chapter name on the inner side.
+
+The text is set to 11 point by default with single line spacing, again, you can tune the text size and spacing should you want or need to using the options at the very start of \file{main.tex}. The spacing can be changed similarly by replacing the \option{singlespacing} with \option{onehalfspacing} or \option{doublespacing}.
+
+\subsection{Using US Letter Paper}
+
+The paper size used in the template is A4, which is the standard size in Europe. If you are using this thesis template elsewhere and particularly in the United States, then you may have to change the A4 paper size to the US Letter size. This can be done in the margins settings section in \file{main.tex}.
+
+Due to the differences in the paper size, the resulting margins may be different to what you like or require (as it is common for institutions to dictate certain margin sizes). If this is the case, then the margin sizes can be tweaked by modifying the values in the same block as where you set the paper size. Now your document should be set up for US Letter paper size with suitable margins.
+
+\subsection{References}
+
+The \code{biblatex} package is used to format the bibliography and inserts references such as this one \parencite{Reference1}. The options used in the \file{main.tex} file mean that the in-text citations of references are formatted with the author(s) listed with the date of the publication. Multiple references are separated by semicolons (e.g. \parencite{Reference2, Reference1}) and references with more than three authors only show the first author with \emph{et al.} indicating there are more authors (e.g. \parencite{Reference3}). This is done automatically for you. To see how you use references, have a look at the \file{Chapter1.tex} source file. Many reference managers allow you to simply drag the reference into the document as you type.
+
+Scientific references should come \emph{before} the punctuation mark if there is one (such as a comma or period). The same goes for footnotes\footnote{Such as this footnote, here down at the bottom of the page.}. You can change this but the most important thing is to keep the convention consistent throughout the thesis. Footnotes themselves should be full, descriptive sentences (beginning with a capital letter and ending with a full stop). The APA6 states: \enquote{Footnote numbers should be superscripted, [...], following any punctuation mark except a dash.} The Chicago manual of style states: \enquote{A note number should be placed at the end of a sentence or clause. The number follows any punctuation mark except the dash, which it precedes. It follows a closing parenthesis.}
+
+The bibliography is typeset with references listed in alphabetical order by the first author's last name. This is similar to the APA referencing style. To see how \LaTeX{} typesets the bibliography, have a look at the very end of this document (or just click on the reference number links in in-text citations).
+
+\subsubsection{A Note on bibtex}
+
+The bibtex backend used in the template by default does not correctly handle unicode character encoding (i.e. "international" characters). You may see a warning about this in the compilation log and, if your references contain unicode characters, they may not show up correctly or at all. The solution to this is to use the biber backend instead of the outdated bibtex backend. This is done by finding this in \file{main.tex}: \option{backend=bibtex} and changing it to \option{backend=biber}. You will then need to delete all auxiliary BibTeX files and navigate to the template directory in your terminal (command prompt). Once there, simply type \code{biber main} and biber will compile your bibliography. You can then compile \file{main.tex} as normal and your bibliography will be updated. An alternative is to set up your LaTeX editor to compile with biber instead of bibtex, see \href{http://tex.stackexchange.com/questions/154751/biblatex-with-biber-configuring-my-editor-to-avoid-undefined-citations/}{here} for how to do this for various editors.
+
+\subsection{Tables}
+
+Tables are an important way of displaying your results, below is an example table which was generated with this code:
+
+{\small
+\begin{verbatim}
+\begin{table}
+\caption{The effects of treatments X and Y on the four groups studied.}
+\label{tab:treatments}
+\centering
+\begin{tabular}{l l l}
+\toprule
+\tabhead{Groups} & \tabhead{Treatment X} & \tabhead{Treatment Y} \\
+\midrule
+1 & 0.2 & 0.8\\
+2 & 0.17 & 0.7\\
+3 & 0.24 & 0.75\\
+4 & 0.68 & 0.3\\
+\bottomrule\\
+\end{tabular}
+\end{table}
+\end{verbatim}
+}
+
+\begin{table}
+\caption{The effects of treatments X and Y on the four groups studied.}
+\label{tab:treatments}
+\centering
+\begin{tabular}{l l l}
+\toprule
+\tabhead{Groups} & \tabhead{Treatment X} & \tabhead{Treatment Y} \\
+\midrule
+1 & 0.2 & 0.8\\
+2 & 0.17 & 0.7\\
+3 & 0.24 & 0.75\\
+4 & 0.68 & 0.3\\
+\bottomrule\\
+\end{tabular}
+\end{table}
+
+You can reference tables with \verb|\ref{<label>}| where the label is defined within the table environment. See \file{Chapter1.tex} for an example of the label and citation (e.g. Table~\ref{tab:treatments}).
+
+\subsection{Figures}
+
+There will hopefully be many figures in your thesis (that should be placed in the \emph{Figures} folder). The way to insert figures into your thesis is to use a code template like this:
+\begin{verbatim}
+\begin{figure}
+\centering
+\includegraphics{Figures/Electron}
+\decoRule
+\caption[An Electron]{An electron (artist's impression).}
+\label{fig:Electron}
+\end{figure}
+\end{verbatim}
+Also look in the source file. Putting this code into the source file produces the picture of the electron that you can see in the figure below.
+
+\begin{figure}[th]
+\centering
+\includegraphics{Figures/Electron}
+\decoRule
+\caption[An Electron]{An electron (artist's impression).}
+\label{fig:Electron}
+\end{figure}
+
+Sometimes figures don't always appear where you write them in the source. The placement depends on how much space there is on the page for the figure. Sometimes there is not enough room to fit a figure directly where it should go (in relation to the text) and so \LaTeX{} puts it at the top of the next page. Positioning figures is the job of \LaTeX{} and so you should only worry about making them look good!
+
+Figures usually should have captions just in case you need to refer to them (such as in Figure~\ref{fig:Electron}). The \verb|\caption| command contains two parts, the first part, inside the square brackets is the title that will appear in the \emph{List of Figures}, and so should be short. The second part in the curly brackets should contain the longer and more descriptive caption text.
+
+The \verb|\decoRule| command is optional and simply puts an aesthetic horizontal line below the image. If you do this for one image, do it for all of them.
+
+\LaTeX{} is capable of using images in pdf, jpg and png format.
+
+\subsection{Typesetting mathematics}
+
+If your thesis is going to contain heavy mathematical content, be sure that \LaTeX{} will make it look beautiful, even though it won't be able to solve the equations for you.
+
+The \enquote{Not So Short Introduction to \LaTeX} (available on \href{http://www.ctan.org/tex-archive/info/lshort/english/lshort.pdf}{CTAN}) should tell you everything you need to know for most cases of typesetting mathematics. If you need more information, a much more thorough mathematical guide is available from the AMS called, \enquote{A Short Math Guide to \LaTeX} and can be downloaded from:
+\url{ftp://ftp.ams.org/pub/tex/doc/amsmath/short-math-guide.pdf}
+
+There are many different \LaTeX{} symbols to remember, luckily you can find the most common symbols in \href{http://ctan.org/pkg/comprehensive}{The Comprehensive \LaTeX~Symbol List}.
+
+You can write an equation, which is automatically given an equation number by \LaTeX{} like this:
+\begin{verbatim}
+\begin{equation}
+E = mc^{2}
+\label{eqn:Einstein}
+\end{equation}
+\end{verbatim}
+
+This will produce Einstein's famous energy-matter equivalence equation:
+\begin{equation}
+E = mc^{2}
+\label{eqn:Einstein}
+\end{equation}
+
+All equations you write (which are not in the middle of paragraph text) are automatically given equation numbers by \LaTeX{}. If you don't want a particular equation numbered, use the unnumbered form:
+\begin{verbatim}
+\[ a^{2}=4 \]
+\end{verbatim}
+
+%----------------------------------------------------------------------------------------
+
+\section{Sectioning and Subsectioning}
+
+You should break your thesis up into nice, bite-sized sections and subsections. \LaTeX{} automatically builds a table of Contents by looking at all the \verb|\chapter{}|, \verb|\section{}| and \verb|\subsection{}| commands you write in the source.
+
+The Table of Contents should only list the sections to three (3) levels. A \verb|chapter{}| is level zero (0). A \verb|\section{}| is level one (1) and so a \verb|\subsection{}| is level two (2). In your thesis it is likely that you will even use a \verb|subsubsection{}|, which is level three (3). The depth to which the Table of Contents is formatted is set within \file{MastersDoctoralThesis.cls}. If you need this changed, you can do it in \file{main.tex}.
+
+%----------------------------------------------------------------------------------------
+
+\section{In Closing}
+
+You have reached the end of this mini-guide. You can now rename or overwrite this pdf file and begin writing your own \file{Chapter1.tex} and the rest of your thesis. The easy work of setting up the structure and framework has been taken care of for you. It's now your job to fill it out!
+
+Good luck and have lots of fun!
+
+\begin{flushright}
+Guide written by ---\\
+Sunil Patel: \href{http://www.sunilpatel.co.uk}{www.sunilpatel.co.uk}\\
+Vel: \href{http://www.LaTeXTemplates.com}{LaTeXTemplates.com}
+\end{flushright}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/Chapters/Chapter2.aux Sun Mar 20 23:32:08 2022 +0000
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+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/Chapters/Chapter2.tex Sun Mar 20 23:32:08 2022 +0000
@@ -0,0 +1,69 @@
+% Chapter Template
+
+\chapter{Chapter Title Here} % Main chapter title
+
+\label{ChapterX} % Change X to a consecutive number; for referencing this chapter elsewhere, use \ref{ChapterX}
+
+%----------------------------------------------------------------------------------------
+% SECTION 1
+%----------------------------------------------------------------------------------------
+
+\section{Properties of $\backslash c$}
+
+To have a clear idea of what we can and
+need to prove about the algorithms involving
+Brzozowski's derivatives, there are a few
+properties we need to be clear about
+it.
+\subsection{function $\backslash c$ is not 1-to-1}
+\begin{center}
+The derivative $w.r.t$ character $c$ is not one-to-one.
+Formally,
+ $\exists r_1 \;r_2. r_1 \neq r_2 \mathit{and} r_1 \backslash c = r_2 \backslash c$
+\end{center}
+This property is trivially true for the
+character regex example:
+\begin{center}
+ $r_1 = e; \; r_2 = d;\; r_1 \backslash c = \ZERO = r_2 \backslash c$
+\end{center}
+But apart from the cases where the derivative
+output is $\ZERO$, are there non-trivial results
+of derivatives which contain strings?
+The answer is yes.
+For example,
+\begin{center}
+ Let $r_1 = a^*b\;\quad r_2 = (a\cdot a^*)\cdot b + b$.\\
+ where $a$ is not nullable.\\
+ $r_1 \backslash c = ((a \backslash c)\cdot a^*)\cdot c + b \backslash c$\\
+ $r_2 \backslash c = ((a \backslash c)\cdot a^*)\cdot c + b \backslash c$
+\end{center}
+We start with two syntactically different regexes,
+and end up with the same derivative result, which is
+a "meaningful" regex because it contains strings.
+We have rediscovered Arden's lemma:\\
+\begin{center}
+ $A^*B = A\cdot A^* \cdot B + B$
+\end{center}
+
+
+%-----------------------------------
+% SUBSECTION 1
+%-----------------------------------
+\subsection{Subsection 1}
+
+Nunc posuere quam at lectus tristique eu ultrices augue venenatis. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Aliquam erat volutpat. Vivamus sodales tortor eget quam adipiscing in vulputate ante ullamcorper. Sed eros ante, lacinia et sollicitudin et, aliquam sit amet augue. In hac habitasse platea dictumst.
+
+%-----------------------------------
+% SUBSECTION 2
+%-----------------------------------
+
+\subsection{Subsection 2}
+Morbi rutrum odio eget arcu adipiscing sodales. Aenean et purus a est pulvinar pellentesque. Cras in elit neque, quis varius elit. Phasellus fringilla, nibh eu tempus venenatis, dolor elit posuere quam, quis adipiscing urna leo nec orci. Sed nec nulla auctor odio aliquet consequat. Ut nec nulla in ante ullamcorper aliquam at sed dolor. Phasellus fermentum magna in augue gravida cursus. Cras sed pretium lorem. Pellentesque eget ornare odio. Proin accumsan, massa viverra cursus pharetra, ipsum nisi lobortis velit, a malesuada dolor lorem eu neque.
+
+%----------------------------------------------------------------------------------------
+% SECTION 2
+%----------------------------------------------------------------------------------------
+
+\section{Main Section 2}
+
+Sed ullamcorper quam eu nisl interdum at interdum enim egestas. Aliquam placerat justo sed lectus lobortis ut porta nisl porttitor. Vestibulum mi dolor, lacinia molestie gravida at, tempus vitae ligula. Donec eget quam sapien, in viverra eros. Donec pellentesque justo a massa fringilla non vestibulum metus vestibulum. Vestibulum in orci quis felis tempor lacinia. Vivamus ornare ultrices facilisis. Ut hendrerit volutpat vulputate. Morbi condimentum venenatis augue, id porta ipsum vulputate in. Curabitur luctus tempus justo. Vestibulum risus lectus, adipiscing nec condimentum quis, condimentum nec nisl. Aliquam dictum sagittis velit sed iaculis. Morbi tristique augue sit amet nulla pulvinar id facilisis ligula mollis. Nam elit libero, tincidunt ut aliquam at, molestie in quam. Aenean rhoncus vehicula hendrerit.
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/Chapters/Chapter3.aux Sun Mar 20 23:32:08 2022 +0000
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/Chapters/Chapter3.tex Sun Mar 20 23:32:08 2022 +0000
@@ -0,0 +1,51 @@
+% Chapter Template
+
+\chapter{Common Identities In Simplification-Related Functions} % Main chapter title
+
+\label{ChapterX} % Change X to a consecutive number; for referencing this chapter elsewhere, use \ref{ChapterX}
+
+
+
+%----------------------------------------------------------------------------------------
+% SECTION 1
+%----------------------------------------------------------------------------------------
+
+\section{Idempotency of $\simp$}
+
+\begin{equation}
+ \simp \;r = \simp\; \simp \; r
+\end{equation}
+This property means we do not have to repeatedly
+apply simplification in each step, which justifies
+our definition of $\blexersimp$.
+It will also be useful in future proofs where properties such as
+closed forms are needed.
+The proof is by structural induction on $r$.
+
+%-----------------------------------
+% SUBSECTION 1
+%-----------------------------------
+\subsection{Syntactic Equivalence Under $\simp$}
+We prove that minor differences can be annhilated
+by $\simp$.
+For example,
+\begin{center}
+$\simp \;(\simpALTs\; (\map \;(\_\backslash \; x)\; (\distinct \; \mathit{rs}\; \phi))) =
+ \simp \;(\simpALTs \;(\distinct \;(\map \;(\_ \backslash\; x) \; \mathit{rs}) \; \phi))$
+\end{center}
+
+
+%-----------------------------------
+% SUBSECTION 2
+%-----------------------------------
+
+\subsection{Subsection 2}
+Morbi rutrum odio eget arcu adipiscing sodales. Aenean et purus a est pulvinar pellentesque. Cras in elit neque, quis varius elit. Phasellus fringilla, nibh eu tempus venenatis, dolor elit posuere quam, quis adipiscing urna leo nec orci. Sed nec nulla auctor odio aliquet consequat. Ut nec nulla in ante ullamcorper aliquam at sed dolor. Phasellus fermentum magna in augue gravida cursus. Cras sed pretium lorem. Pellentesque eget ornare odio. Proin accumsan, massa viverra cursus pharetra, ipsum nisi lobortis velit, a malesuada dolor lorem eu neque.
+
+%----------------------------------------------------------------------------------------
+% SECTION 2
+%----------------------------------------------------------------------------------------
+
+\section{Main Section 2}
+
+Sed ullamcorper quam eu nisl interdum at interdum enim egestas. Aliquam placerat justo sed lectus lobortis ut porta nisl porttitor. Vestibulum mi dolor, lacinia molestie gravida at, tempus vitae ligula. Donec eget quam sapien, in viverra eros. Donec pellentesque justo a massa fringilla non vestibulum metus vestibulum. Vestibulum in orci quis felis tempor lacinia. Vivamus ornare ultrices facilisis. Ut hendrerit volutpat vulputate. Morbi condimentum venenatis augue, id porta ipsum vulputate in. Curabitur luctus tempus justo. Vestibulum risus lectus, adipiscing nec condimentum quis, condimentum nec nisl. Aliquam dictum sagittis velit sed iaculis. Morbi tristique augue sit amet nulla pulvinar id facilisis ligula mollis. Nam elit libero, tincidunt ut aliquam at, molestie in quam. Aenean rhoncus vehicula hendrerit.
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/Chapters/ChapterTemplate.tex Sun Mar 20 23:32:08 2022 +0000
@@ -0,0 +1,35 @@
+% Chapter Template
+
+\chapter{Chapter Title Here} % Main chapter title
+
+\label{ChapterX} % Change X to a consecutive number; for referencing this chapter elsewhere, use \ref{ChapterX}
+
+%----------------------------------------------------------------------------------------
+% SECTION 1
+%----------------------------------------------------------------------------------------
+
+\section{Main Section 1}
+
+Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aliquam ultricies lacinia euismod. Nam tempus risus in dolor rhoncus in interdum enim tincidunt. Donec vel nunc neque. In condimentum ullamcorper quam non consequat. Fusce sagittis tempor feugiat. Fusce magna erat, molestie eu convallis ut, tempus sed arcu. Quisque molestie, ante a tincidunt ullamcorper, sapien enim dignissim lacus, in semper nibh erat lobortis purus. Integer dapibus ligula ac risus convallis pellentesque.
+
+%-----------------------------------
+% SUBSECTION 1
+%-----------------------------------
+\subsection{Subsection 1}
+
+Nunc posuere quam at lectus tristique eu ultrices augue venenatis. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Aliquam erat volutpat. Vivamus sodales tortor eget quam adipiscing in vulputate ante ullamcorper. Sed eros ante, lacinia et sollicitudin et, aliquam sit amet augue. In hac habitasse platea dictumst.
+
+%-----------------------------------
+% SUBSECTION 2
+%-----------------------------------
+
+\subsection{Subsection 2}
+Morbi rutrum odio eget arcu adipiscing sodales. Aenean et purus a est pulvinar pellentesque. Cras in elit neque, quis varius elit. Phasellus fringilla, nibh eu tempus venenatis, dolor elit posuere quam, quis adipiscing urna leo nec orci. Sed nec nulla auctor odio aliquet consequat. Ut nec nulla in ante ullamcorper aliquam at sed dolor. Phasellus fermentum magna in augue gravida cursus. Cras sed pretium lorem. Pellentesque eget ornare odio. Proin accumsan, massa viverra cursus pharetra, ipsum nisi lobortis velit, a malesuada dolor lorem eu neque.
+
+%----------------------------------------------------------------------------------------
+% SECTION 2
+%----------------------------------------------------------------------------------------
+
+\section{Main Section 2}
+
+Sed ullamcorper quam eu nisl interdum at interdum enim egestas. Aliquam placerat justo sed lectus lobortis ut porta nisl porttitor. Vestibulum mi dolor, lacinia molestie gravida at, tempus vitae ligula. Donec eget quam sapien, in viverra eros. Donec pellentesque justo a massa fringilla non vestibulum metus vestibulum. Vestibulum in orci quis felis tempor lacinia. Vivamus ornare ultrices facilisis. Ut hendrerit volutpat vulputate. Morbi condimentum venenatis augue, id porta ipsum vulputate in. Curabitur luctus tempus justo. Vestibulum risus lectus, adipiscing nec condimentum quis, condimentum nec nisl. Aliquam dictum sagittis velit sed iaculis. Morbi tristique augue sit amet nulla pulvinar id facilisis ligula mollis. Nam elit libero, tincidunt ut aliquam at, molestie in quam. Aenean rhoncus vehicula hendrerit.
\ No newline at end of file
Binary file PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/Figures/Electron.pdf has changed
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/MastersDoctoralThesis.cls Sun Mar 20 23:32:08 2022 +0000
@@ -0,0 +1,544 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Masters/Doctoral Thesis
+% Class File
+% Version 1.6 (27/8/17)
+%
+% This class was downloaded from:
+% http://www.LaTeXTemplates.com
+%
+% Authors:
+% Vel (vel@latextemplates.com)
+% Johannes Böttcher
+%
+% Notes:
+% 1) This class file defines the structure and layout of the template file (main.tex).
+% 2) It has been written in such a way that under most circumstances you should not need
+% to edit it; updating it to a newer version will be harder. If you do make changes, please change the name of
+% the file and add comments to make your changes more visible.
+%
+% Class license:
+% LPPL v1.3c (http://www.latex-project.org/lppl)
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%----------------------------------------------------------------------------------------
+% CLASS DEFINITION AND PARAMETERS
+%----------------------------------------------------------------------------------------
+
+\NeedsTeXFormat{LaTeX2e}[1996/12/01]
+\newcommand{\classname}{MastersDoctoralThesis}
+\ProvidesClass{\classname}[2017/08/27 v1.6 LaTeXTemplates.com]
+\providecommand{\baseclass}{book}
+\RequirePackage{etoolbox}
+\RequirePackage{xparse}
+\newbool{nolistspace}
+\newbool{chapteroneline}
+\newbool{listtoc}
+\newbool{toctoc}
+\newbool{parskip}
+\newbool{hyperrefsupport}
+\booltrue{hyperrefsupport}
+\newbool{headsepline}
+\newbool{consistentlayout}
+
+\DeclareOption{nohyperref}{\boolfalse{hyperrefsupport}}
+\DeclareOption{nolistspacing}{\booltrue{nolistspace}}
+\DeclareOption{liststotoc}{\booltrue{listtoc}}
+\DeclareOption{chapterinoneline}{\booltrue{chapteroneline}}
+\DeclareOption{toctotoc}{\booltrue{toctoc}}
+\DeclareOption{parskip}{\booltrue{parskip}}
+\DeclareOption{headsepline}{\booltrue{headsepline}}
+\DeclareOption{consistentlayout}{\booltrue{consistentlayout}}
+\DeclareOption*{\PassOptionsToClass{\CurrentOption}{\baseclass}}
+
+\ProcessOptions\relax
+
+\LoadClass{\baseclass}
+
+% Simple interface for the user to customize the chapter titles
+\ProvideDocumentCommand{\abovechapterskip}{}{\vspace*{20pt}}
+\ProvideDocumentCommand{\chapterbelowskip}{}{\vspace*{40pt}}
+\ProvideDocumentCommand{\chapterinbetweenskip}{}{\vspace*{20pt}}
+\ProvideDocumentCommand{\autodot}{}{}
+\ProvideDocumentCommand{\mdtChapapp}{}{}
+\ProvideDocumentCommand{\chapteralign}{}{\raggedright}
+\ProvideDocumentCommand{\chapterfont}{}{\Huge\bfseries}
+\ProvideDocumentCommand{\chapterprefixfont}{}{\LARGE\bfseries}
+\DeclareDocumentCommand{\@makechapterhead}{ m }{%
+ \abovechapterskip
+ {\parindent \z@ \chapteralign \normalfont
+ \ifnum \c@secnumdepth >\m@ne
+ \if@mainmatter
+ \ifbool{chapteroneline}{%
+ \chapterfont \mdtChapapp\thechapter\autodot\enspace
+ }{%
+ \chapterprefixfont \@chapapp\space \thechapter
+ \par\nobreak
+ \chapterinbetweenskip
+ }%
+ \fi
+ \fi
+ \interlinepenalty\@M%
+ \chapterfont #1\par\nobreak
+ \chapterbelowskip
+ }
+ \thispagestyle{\chapter@p@gestyle}
+}
+\def\@makeschapterhead#1{%
+ \abovechapterskip
+ {\parindent \z@ \chapteralign
+ \normalfont
+ \interlinepenalty\@M
+ \chapterfont #1\par\nobreak
+ \chapterbelowskip
+ }
+ \thispagestyle{\chapter@p@gestyle}
+}
+
+
+% Addchap provides unnumbered chapters with an entry in the table of contents as well as an updated header
+\ProvideDocumentCommand{\addchap}{ s o m }{%
+ \chapter*{#3}%
+ \markboth{}{}%
+ \IfBooleanTF{#1}{%
+ }{%
+ \IfNoValueTF{#2}{%
+ \addchaptertocentry{#3}%
+ \markboth{\MakeMarkcase{#3}}{\MakeMarkcase{#3}}%
+ }{%
+ \addchaptertocentry{#2}%
+ \markboth{\MakeMarkcase{#2}}{\MakeMarkcase{#2}}%
+ }%
+ }%
+}%
+
+\ProvideDocumentCommand{\addsec}{ s o m }{%
+ \section*{#3}%
+ \markright{}%
+ \IfBooleanTF{#1}{%
+ }{%
+ \IfNoValueTF{#2}{%
+ \addcontentsline{toc}{section}{#3}%
+ \markright{\MakeMarkcase{#3}}%%
+ }{%
+ \addcontentsline{toc}{section}{#2}%
+ \markright{\MakeMarkcase{#2}}%
+ }%
+ }%
+}%
+
+%----------------------------------------------------------------------------------------
+% CLASS OPTIONS
+%----------------------------------------------------------------------------------------
+
+\ifbool{parskip}{\RequirePackage{parskip}} % If the parskip option is passed to the class, require the parskip package
+
+
+\ifbool{listtoc}{% If the liststotoc option has been passed to the class, add the lists to the table of contents
+ \patchcmd{\listoftables}{\@starttoc{lot}}{%
+ \addchaptertocentry{\listtablename}\@starttoc{lot}%
+ }{}{}%
+ \patchcmd{\listoffigures}{\@starttoc{lof}}{%
+ \addchaptertocentry{\listfigurename}\@starttoc{lof}%
+ }{}{}%
+}
+
+\ifbool{toctoc}{% If the toctotoc options has been passed to the class, add the table of contents to the table of contents
+ \patchcmd{\tableofcontents}{\@starttoc{toc}%
+}{%
+ \addchaptertocentry{\contentsname}\@starttoc{toc}}{}{}%
+}
+
+\patchcmd{\tableofcontents}{\MakeUppercase}{\MakeMarkcase}{}{}
+\patchcmd{\tableofcontents}{\MakeUppercase}{\MakeMarkcase}{}{}
+\patchcmd{\listoffigures}{\MakeUppercase}{\MakeMarkcase}{}{}
+\patchcmd{\listoffigures}{\MakeUppercase}{\MakeMarkcase}{}{}
+\patchcmd{\listoftables}{\MakeUppercase}{\MakeMarkcase}{}{}
+\patchcmd{\listoftables}{\MakeUppercase}{\MakeMarkcase}{}{}
+
+% If the option `nolistspacing' is given, the spacing in the different lists is reduced to single spacing. This option is only useful, if the spacing of the document has been changed to onehalfspacing or doublespacing.
+\ifbool{nolistspace}{
+ \patchcmd{\listoffigures}{%
+ \@starttoc{lof}
+ }{%
+ \begingroup%
+ \singlespace\@starttoc{lof}\endgroup%
+ }{}{}%
+ \patchcmd{\listoftables}{%
+ \@starttoc{lot}
+ }{%
+ \begingroup%
+ \singlespace\@starttoc{lot}\endgroup%
+ }{}{}%
+ \patchcmd{\tableofcontents}{%
+ \@starttoc{toc}
+ }{%
+ \begingroup%
+ \singlespace\@starttoc{toc}\endgroup%
+ }{}{}%
+}{}
+
+
+%----------------------------------------------------------------------------------------
+% REQUIRED PACKAGES
+%----------------------------------------------------------------------------------------
+
+\RequirePackage{babel} % Required for automatically changing names of document elements to languages besides english
+
+\RequirePackage{scrbase} % Required for handling language-dependent names of sections/document elements
+
+\RequirePackage{scrhack} % Loads fixes for various packages
+
+\RequirePackage{setspace} % Required for changing line spacing
+
+\RequirePackage{longtable} % Required for tables that span multiple pages (used in the symbols, abbreviations and physical constants pages)
+
+\RequirePackage{siunitx} % Required for \SI commands
+
+\RequirePackage{graphicx} % Required to include images
+\graphicspath{{Figures/}{./}} % Specifies where to look for included images
+
+\RequirePackage{booktabs} % Required for better table rules
+
+\RequirePackage{caption} % Required for customising the captions
+\captionsetup{justification=centerlast,font=small,labelfont=sc,margin=50pt}
+
+%----------------------------------------------------------------------------------------
+% DEFINE CUSTOM THESIS INFORMATION COMMANDS
+%----------------------------------------------------------------------------------------
+
+\NewDocumentCommand{\thesistitle} { o m }{%
+ \IfValueTF{#1}{\def\shorttitle{#1}}{\def\shorttitle{#2}}%
+ \def\@title{#2}%
+ \def\ttitle{#2}%
+}
+\DeclareDocumentCommand{\author}{m}{\newcommand{\authorname}{#1}\renewcommand{\@author}{#1}}
+\NewDocumentCommand{\supervisor}{m}{\newcommand{\supname}{#1}}
+\NewDocumentCommand{\examiner}{m}{\newcommand{\examname}{#1}}
+\NewDocumentCommand{\degree}{m}{\newcommand{\degreename}{#1}}
+\NewDocumentCommand{\addresses}{m}{\newcommand{\addressname}{#1}}
+\NewDocumentCommand{\university}{m}{\newcommand{\univname}{#1}}
+\NewDocumentCommand{\department}{m}{\newcommand{\deptname}{#1}}
+\NewDocumentCommand{\group}{m}{\newcommand{\groupname}{#1}}
+\NewDocumentCommand{\faculty}{m}{\newcommand{\facname}{#1}}
+\NewDocumentCommand{\subject}{m}{\newcommand{\subjectname}{#1}}
+\NewDocumentCommand{\keywords}{m}{\newcommand{\keywordnames}{#1}}
+
+\newcommand{\checktoopen}{% New command to move content to the next page which prints to the next odd page if twosided mode is active
+ \if@openright\cleardoublepage\else\clearpage\fi
+ \ifdef{\phantomsection}{\phantomsection}{}% The \phantomsection command is necessary for hyperref to jump to the correct page
+}
+
+\NewDocumentCommand{\bhrule}{}{\typeout{--------------------}}
+\NewDocumentCommand{\tttypeout}{m}{\bhrule\typeout{\space #1}\bhrule}
+
+\newcommand{\HRule}{\rule{.9\linewidth}{.6pt}} % New command to make the lines in the title page
+\newcommand{\decoRule}{\rule{.8\textwidth}{.4pt}} % New command for a rule to be used under figures
+
+\setcounter{tocdepth}{3} % The depth to which the document sections are printed to the table of contents
+\ProvideDocumentCommand{\addchaptertocentry}{ m }{%
+ \addcontentsline{toc}{chapter}{#1}%
+}
+
+%----------------------------------------------------------------------------------------
+% COLOURS
+%----------------------------------------------------------------------------------------
+
+\usepackage{xcolor} % Required for specifying custom colours
+
+\colorlet{mdtRed}{red!50!black}
+
+%----------------------------------------------------------------------------------------
+% MARGINS
+%----------------------------------------------------------------------------------------
+
+\RequirePackage{geometry}
+\geometry{
+ headheight=4ex,
+ includehead,
+ includefoot
+}
+
+\raggedbottom
+
+%----------------------------------------------------------------------------------------
+% PENALTIES
+%----------------------------------------------------------------------------------------
+
+\doublehyphendemerits=10000 % No consecutive line hyphens
+\brokenpenalty=10000 % No broken words across columns/pages
+\widowpenalty=9999 % Almost no widows at bottom of page
+\clubpenalty=9999 % Almost no orphans at top of page
+\interfootnotelinepenalty=9999 % Almost never break footnotes
+
+%----------------------------------------------------------------------------------------
+% HEADERS AND FOOTERS
+%----------------------------------------------------------------------------------------
+
+\RequirePackage[markcase=used]{scrlayer-scrpage}
+\providepairofpagestyles{thesisSimple}{%
+ \clearpairofpagestyles%
+ \automark[chapter]{chapter}
+ \ihead{\headmark}% Inner header
+ \ohead[\pagemark]{\pagemark}% Outer header
+}
+\ifoot{}% Inner footer
+\ofoot{}% Outer footer
+\pagestyle{thesisSimple}
+\providepairofpagestyles[thesisSimple]{thesis}{%
+ \automark*[section]{}%
+}
+\providepairofpagestyles[thesisSimple]{review}{%
+ \ofoot[\shorttitle/\authorname]{\shorttitle/\authorname}
+ \ifoot[\today]{\today}
+}
+\pagestyle{thesis}
+\ifbool{headsepline}{\KOMAoption{headsepline}{true}}{}
+\PreventPackageFromLoading[\ClassError{\classname}{Package `fancyhdr' is
+incompatible\MessageBreak with this class}{The pagesyles are defined
+ using package `scrlayer-scrpage', please consult the\MessageBreak
+KOMA-script documentation for details.}]{fancyhdr}
+
+
+\newcommand{\blank@p@gestyle}{empty}
+\newcommand{\chapter@p@gestyle}{plain}
+\NewDocumentCommand{\blankpagestyle}{ m }{%
+ \ClassWarning{\classname}{\string\blankpagestyle\space is
+ obsolete,\MessageBreak use \string\setblankpagestyle \space instead}\renewcommand{\blank@p@gestyle}{}{#1}
+}
+\NewDocumentCommand{\setblankpagestyle}{ m }{\renewcommand{\blank@p@gestyle}{#1}}
+\NewDocumentCommand{\setchapterpagestyle}{ m }{\renewcommand{\chapter@p@gestyle}{#1}}
+
+\DeclareDocumentCommand\cleardoublepage{}{\clearpage\if@twoside \ifodd\c@page\else
+ \hbox{}
+ \thispagestyle{\blank@p@gestyle}
+ \newpage
+ \if@twocolumn\hbox{}\newpage\fi\fi\fi%
+}
+
+%----------------------------------------------------------------------------------------
+% ABBREVIATIONS PAGE DESIGN
+%----------------------------------------------------------------------------------------
+
+\newcommand{\abbrevname}{List of Abbreviations}
+\providecaptionname{english,british,american}{\abbrevname}{List of Abbreviations}
+\providecaptionname{ngerman,german,austrian,naustrian}{\abbrevname}{Abk\"urzungsverzeichnis}
+\NewDocumentEnvironment{abbreviations}{ m }{%
+ \ifbool{nolistspace}{\begingroup\singlespacing}{}
+ \ifbool{listtoc}{\addchap{\abbrevname}}{\addchap*{\abbrevname}}
+ \begin{longtable}{#1}
+ }{%
+ \end{longtable}
+ \addtocounter{table}{-1}% Don't count this table as one of the document tables
+ \ifbool{nolistspace}{\endgroup}{}
+}
+
+%----------------------------------------------------------------------------------------
+% ABSTRACT PAGE DESIGN
+%----------------------------------------------------------------------------------------
+
+\DeclareDocumentCommand{\abstractauthorfont}{}{}
+\DeclareDocumentCommand{\abstracttitlefont}{}{}
+\newcommand{\byname}{by}
+\newcommand{\abstractname}{Abstract}
+\providecaptionname{german,ngerman,austrian,naustrian}{\byname}{von}
+\providecaptionname{american,australian,british,canadian,english,newzealand,UKenglish,USenglish}{\byname}{by}
+\ifbool{consistentlayout}{
+ \DeclareDocumentEnvironment{abstract}{ O{} }{%
+ \addchap*{\abstractname}%
+ {\chapteralign\normalsize\abstractauthorfont \authorname \par}% Author name
+ \vspace{\baselineskip}
+ {\chapteralign\parbox{.7\linewidth}{\chapteralign\normalsize\itshape\abstracttitlefont\@title}\par}% Thesis title
+ \bigskip\noindent\ignorespaces
+ }%
+ {}%end alt-abstract
+}{%
+ \DeclareDocumentEnvironment{abstract}{ O{\null\vfill} }{
+ \checktoopen
+ \tttypeout{\abstractname}
+ #1%added to be able to have abstract more than one page long
+ \thispagestyle{plain}
+ \begin{center}
+ {\normalsize \MakeUppercase{\univname} \par}% University name in capitals
+ \bigskip
+ {\huge\textit{\abstractname} \par}
+ \bigskip
+ {\normalsize \facname \par}% Faculty name
+ {\normalsize \deptname \par}% Department name
+ \bigskip
+ {\normalsize \degreename\par}% Degree name
+ \bigskip
+ {\normalsize\bfseries \@title \par}% Thesis title
+ \medskip
+ {\normalsize \byname{} \authorname \par}% Author name
+ \bigskip
+ \end{center}
+ }
+ {
+ \vfill\null
+ }
+}
+
+\DeclareDocumentEnvironment{extraAbstract}{ O{\null\vfill} }{
+ \checktoopen
+ \tttypeout{\abstractname}
+ #1%added to be able to have abstract more than one page long
+ \thispagestyle{empty}
+ \begin{center}
+ {\normalsize \MakeUppercase{\univname} \par}% University name in capitals
+ \bigskip
+ {\huge\textit{\abstractname} \par}
+ \bigskip
+ {\normalsize \facname \par}% Faculty name
+ {\normalsize \deptname \par}% Department name
+ \bigskip
+ {\normalsize \degreename\par}% Degree name
+ \bigskip
+ {\normalsize\bfseries \@title \par}% Thesis title
+ \medskip
+ {\normalsize \byname{} \authorname \par}% Author name
+ \bigskip
+ \end{center}
+}
+{
+ \vfill\null
+}
+
+%----------------------------------------------------------------------------------------
+% ACKNOWLEDGEMENTS PAGE DESIGN
+%----------------------------------------------------------------------------------------
+
+\usepackage{xcolor}
+\colorlet{mdtRed}{red!50!black}
+\newcommand{\acknowledgementname}{Acknowledgements}
+\providecaptionname{american,australian,british,canadian,english,newzealand,UKenglish,USenglish} {\acknowledgementname}{Acknowledgements} % Acknowledgement text for English countries
+\providecaptionname{german,ngerman,austrian,naustrian}{\acknowledgementname}{Danksagung} % Acknowledgement text for Germanic countries
+
+\ifbool{consistentlayout}{
+ \DeclareDocumentEnvironment{acknowledgements}{}{%
+ \tttypeout{\acknowledgementname}
+ \addchap*{\acknowledgementname}
+ }
+}
+{
+ \DeclareDocumentEnvironment{acknowledgements}{}{%
+ \checktoopen
+ \tttypeout{\acknowledgementname}
+ \thispagestyle{plain}
+ \begin{center}{\huge\textit{\acknowledgementname}\par}\end{center}
+ }
+ {
+ \vfil\vfil\null
+ }
+}
+
+%----------------------------------------------------------------------------------------
+% DECLARATION PAGE DESIGN
+%----------------------------------------------------------------------------------------
+
+\newcommand{\authorshipname}{Declaration of Authorship}
+\providecaptionname{american,australian,british,canadian,english,newzealand,UKenglish,USenglish}{\authorshipname}{Declaration of Authorship} % Declaration of Authorship text for English countries
+\providecaptionname{german,ngerman,austrian,naustrian}{\authorshipname}{Eidesstattliche Erkl\"arung} % Declaration of Authorship text for Germanic countries
+
+\ifbool{consistentlayout}{
+ \DeclareDocumentEnvironment{declaration}{}{
+ \addchap*{\authorshipname}
+ }{}%
+}{
+ \DeclareDocumentEnvironment{declaration}{}{
+ \checktoopen
+ \tttypeout{\authorshipname}
+ \thispagestyle{plain}
+ \null\vfil
+ {\noindent\huge\bfseries\authorshipname\par\vspace{10pt}}
+ }{}
+}
+
+%----------------------------------------------------------------------------------------
+% DEDICATION PAGE DESIGN
+%----------------------------------------------------------------------------------------
+
+\ifbool{consistentlayout}{
+ \DeclareDocumentCommand{\dedicatory}{
+ m O{\vspace*{.7\textheight} } }{
+ \checktoopen\tttypeout{Dedicatory}
+ \markboth{}{}
+ #2
+ {\hfill\parbox{.4\textwidth}{\flushright#1\par}}
+ }
+}{
+ \newcommand\dedicatory[1]{
+ \checktoopen
+ \tttypeout{Dedicatory}
+ \null\vfil
+ \thispagestyle{plain}
+ \begin{center}{\Large\slshape #1}\end{center}
+ \vfil\null
+ }
+}
+
+
+%----------------------------------------------------------------------------------------
+% PHYSICAL CONSTANTS PAGE DESIGN
+%----------------------------------------------------------------------------------------
+
+\newcommand{\constantsname}{Physical Constants}
+\providecaptionname{english,british,american}{\constantsname}{Physical Constants}
+\providecaptionname{ngerman,german,austrian,naustrian}{\constantsname}{Physikalische Konstanten}
+
+\NewDocumentEnvironment{constants}{ m }{%
+ \ifbool{nolistspace}{\begingroup\singlespacing}{}
+ \ifbool{listtoc}{\addchap{\constantsname}}{\addchap*{\constantsname}}
+ \begin{longtable}{#1}
+ }{%
+ \end{longtable}
+ \addtocounter{table}{-1}% Don't count this table as one of the document tables
+ \ifbool{nolistspace}{\endgroup}{}
+}
+
+%----------------------------------------------------------------------------------------
+% SYMBOLS PAGE DESIGN
+%----------------------------------------------------------------------------------------
+
+\newcommand{\symbolsname}{List of Symbols}
+\providecaptionname{english,british,american}{\symbolsname}{List of Symbols}
+\providecaptionname{ngerman,german,austrian,naustrian}{\symbolsname}{Symbolverzeichnis}
+
+\NewDocumentEnvironment{symbols}{ m }{%
+ \ifbool{nolistspace}{\begingroup\singlespacing}{}
+ \ifbool{listtoc}{\addchap{\symbolsname}}{\addchap*{\symbolsname}}
+ \begin{longtable}{#1}
+ }{%
+ \end{longtable}
+ \addtocounter{table}{-1}% Don't count this table as one of the document tables
+ \ifbool{nolistspace}{\endgroup}{}
+}
+
+%----------------------------------------------------------------------------------------
+
+\ifbool{hyperrefsupport}{% If the nohyperref class option has not been specified
+\AtEndPreamble{\RequirePackage{hyperref}
+\hypersetup{pdfpagemode={UseOutlines},
+bookmarksopen=true,
+bookmarksopenlevel=0,
+hypertexnames=false,
+colorlinks=true,% Set to false to disable coloring links
+citecolor=magenta,% The color of citations
+linkcolor=red,% The color of references to document elements (sections, figures, etc)
+urlcolor=mdtRed,% The color of hyperlinks (URLs)
+pdfstartview={FitV},
+unicode,
+breaklinks=true,
+}
+
+\pdfstringdefDisableCommands{% If there is an explicit linebreak in a section heading (or anything printed to the pdf-bookmarks), it is replaced by a space
+ \let\\\space%
+}
+ }
+}{%nothing
+}
+
+%----------------------------------------------------------------------------------------
+
+\endinput
+% lazyLizardTracer
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/bad-scala.data Sun Mar 20 23:32:08 2022 +0000
@@ -0,0 +1,34 @@
+%% LaTeX2e file `bad-scala.data'
+%% generated by the `filecontents' environment
+%% from source `main' on 2022/03/16.
+%%
+1 0.048028
+2 0.126308
+3 0.169670
+4 0.264180
+5 0.384297
+6 0.612785
+7 0.817211
+8 1.089386
+9 1.363222
+10 1.644981
+11 1.987046
+12 2.416012
+13 2.920956
+14 3.398956
+15 3.739649
+16 4.329977
+17 4.932896
+18 5.633909
+19 6.436107
+20 6.927233
+21 7.441163
+22 8.242139
+23 8.901034
+24 9.680487
+25 10.496226
+26 11.385733
+27 12.247613
+28 13.990491
+29 14.245804
+30 15.206283
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/data.sty Sun Mar 20 23:32:08 2022 +0000
@@ -0,0 +1,123 @@
+% The data files, written on the first run.
+
+
+\begin{filecontents}{re-python2.data}
+1 0.033
+5 0.036
+10 0.034
+15 0.036
+18 0.059
+19 0.084
+20 0.141
+21 0.248
+22 0.485
+23 0.878
+24 1.71
+25 3.40
+26 7.08
+27 14.12
+28 26.69
+\end{filecontents}
+
+
+% JavaScript, example (a*)*b
+\begin{filecontents}{re-js.data}
+5 0.061
+10 0.061
+15 0.061
+20 0.070
+23 0.131
+25 0.308
+26 0.564
+28 1.994
+30 7.648
+31 15.881
+32 32.190
+\end{filecontents}
+
+% Java 8, example (a*)*b
+\begin{filecontents}{re-java.data}
+5 0.00298
+10 0.00418
+15 0.00996
+16 0.01710
+17 0.03492
+18 0.03303
+19 0.05084
+20 0.10177
+21 0.19960
+22 0.41159
+23 0.82234
+24 1.70251
+25 3.36112
+26 6.63998
+27 13.35120
+28 29.81185
+\end{filecontents}
+
+% Java, example (a*)b
+\begin{filecontents}{good-java.data}
+1 1.5633E-5
+2 1.299E-5
+3 1.1451E-5
+4 1.5846E-5
+5 1.9934E-5
+6 2.174E-5
+7 2.7669E-5
+8 2.8657E-5
+9 2.8161E-5
+10 2.8729E-5
+11 3.5367E-5
+12 3.701E-5
+13 3.84E-5
+14 4.1329E-5
+15 4.8116E-5
+16 5.3597E-5
+17 4.6792E-5
+18 5.8618E-5
+19 6.2078E-5
+20 6.4702E-5
+21 6.1464E-5
+22 6.4693E-5
+23 6.1667E-5
+24 7.1466E-5
+25 7.8089E-5
+26 7.4661E-5
+27 7.5628E-5
+28 8.9169E-5
+29 9.4161E-5
+30 9.8494E-5
+\end{filecontents}
+
+\begin{filecontents}{bad-scala.data}
+1 0.048028
+2 0.126308
+3 0.169670
+4 0.264180
+5 0.384297
+6 0.612785
+7 0.817211
+8 1.089386
+9 1.363222
+10 1.644981
+11 1.987046
+12 2.416012
+13 2.920956
+14 3.398956
+15 3.739649
+16 4.329977
+17 4.932896
+18 5.633909
+19 6.436107
+20 6.927233
+21 7.441163
+22 8.242139
+23 8.901034
+24 9.680487
+25 10.496226
+26 11.385733
+27 12.247613
+28 13.990491
+29 14.245804
+30 15.206283
+\end{filecontents}
\ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/example.bib Sun Mar 20 23:32:08 2022 +0000
@@ -0,0 +1,370 @@
+%% This BibTeX bibliography file was created using BibDesk.
+%% https://bibdesk.sourceforge.io/
+
+%% Created for CS TAN at 2022-03-16 16:38:47 +0000
+
+
+%% Saved with string encoding Unicode (UTF-8)
+
+
+
+@inproceedings{RibeiroAgda2017,
+ abstract = {We describe the formalization of a regular expression (RE) parsing algorithm that produces a bit representation of its parse tree in the dependently typed language Agda. The algorithm computes bit-codes using Brzozowski derivatives and we prove that produced codes are equivalent to parse trees ensuring soundness and completeness w.r.t an inductive RE semantics. We include the certified algorithm in a tool developed by us, named verigrep, for regular expression based search in the style of the well known GNU grep. Practical experiments conducted with this tool are reported.},
+ address = {New York, NY, USA},
+ articleno = {4},
+ author = {Ribeiro, Rodrigo and Bois, Andr\'{e} Du},
+ booktitle = {Proceedings of the 21st Brazilian Symposium on Programming Languages},
+ date-modified = {2022-03-16 16:38:47 +0000},
+ doi = {10.1145/3125374.3125381},
+ isbn = {9781450353892},
+ keywords = {Certified algorithms, regular expressions, dependent types, bit-codes},
+ location = {Fortaleza, CE, Brazil},
+ numpages = {8},
+ publisher = {Association for Computing Machinery},
+ series = {SBLP 2017},
+ title = {Certified Bit-Coded Regular Expression Parsing},
+ url = {https://doi.org/10.1145/3125374.3125381},
+ year = {2017},
+ bdsk-url-1 = {https://doi.org/10.1145/3125374.3125381}}
+
+@article{Thompson_1968,
+ author = {Ken Thompson},
+ date-added = {2022-02-23 13:44:42 +0000},
+ date-modified = {2022-02-23 13:44:42 +0000},
+ doi = {10.1145/363347.363387},
+ journal = {Communications of the {ACM}},
+ month = {jun},
+ number = {6},
+ pages = {419--422},
+ publisher = {Association for Computing Machinery ({ACM})},
+ title = {Programming Techniques: Regular expression search algorithm},
+ url = {https://doi.org/10.1145%2F363347.363387},
+ volume = {11},
+ year = 1968,
+ bdsk-url-1 = {https://doi.org/10.1145%2F363347.363387},
+ bdsk-url-2 = {https://doi.org/10.1145/363347.363387}}
+
+@article{17Bir,
+ author = {Asiri Rathnayake and Hayo Thielecke},
+ date-added = {2019-08-18 17:57:30 +0000},
+ date-modified = {2019-08-18 18:00:13 +0000},
+ journal = {arXiv:1405.7058},
+ title = {Static Analysis for Regular Expression Exponential Runtime via Substructural Logics},
+ year = {2017}}
+
+@article{nielson11bcre,
+ author = {Lasse Nielsen, Fritz Henglein},
+ date-added = {2019-07-03 21:09:39 +0000},
+ date-modified = {2019-07-03 21:17:33 +0000},
+ journal = {LATA},
+ title = {Bit-coded Regular Expression Parsing},
+ year = {2011},
+ bdsk-file-1 = {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}}
+
+@misc{SE16,
+ author = {StackStatus},
+ date-added = {2019-06-26 11:28:41 +0000},
+ date-modified = {2019-06-26 16:07:31 +0000},
+ keywords = {ReDos Attack},
+ month = {July},
+ rating = {5},
+ read = {1},
+ title = {Stack Overflow Outage Postmortem},
+ url = {https://stackstatus.net/post/147710624694/outage-postmortem-july-20-2016},
+ year = {2016},
+ bdsk-url-1 = {https://stackstatus.net/post/147710624694/outage-postmortem-july-20-2016}}
+
+@article{HosoyaVouillonPierce2005,
+ author = {H.~Hosoya and J.~Vouillon and B.~C.~Pierce},
+ journal = {ACM Transactions on Programming Languages and Systems (TOPLAS)},
+ number = 1,
+ pages = {46--90},
+ title = {{R}egular {E}xpression {T}ypes for {XML}},
+ volume = 27,
+ year = {2005}}
+
+@misc{POSIX,
+ note = {\url{http://pubs.opengroup.org/onlinepubs/009695399/basedefs/xbd_chap09.html}},
+ title = {{T}he {O}pen {G}roup {B}ase {S}pecification {I}ssue 6 {IEEE} {S}td 1003.1 2004 {E}dition},
+ year = {2004}}
+
+@inproceedings{AusafDyckhoffUrban2016,
+ author = {F.~Ausaf and R.~Dyckhoff and C.~Urban},
+ booktitle = {Proc.~of the 7th International Conference on Interactive Theorem Proving (ITP)},
+ pages = {69--86},
+ series = {LNCS},
+ title = {{POSIX} {L}exing with {D}erivatives of {R}egular {E}xpressions ({P}roof {P}earl)},
+ volume = {9807},
+ year = {2016}}
+
+@article{aduAFP16,
+ author = {F.~Ausaf and R.~Dyckhoff and C.~Urban},
+ issn = {2150-914x},
+ journal = {Archive of Formal Proofs},
+ note = {\url{http://www.isa-afp.org/entries/Posix-Lexing.shtml}, Formal proof development},
+ title = {{POSIX} {L}exing with {D}erivatives of {R}egular {E}xpressions},
+ year = 2016}
+
+@techreport{CrashCourse2014,
+ annote = {draft report},
+ author = {N.~B.~B.~Grathwohl and F.~Henglein and U.~T.~Rasmussen},
+ institution = {University of Copenhagen},
+ title = {{A} {C}rash-{C}ourse in {R}egular {E}xpression {P}arsing and {R}egular {E}xpressions as {T}ypes},
+ year = {2014}}
+
+@inproceedings{Sulzmann2014,
+ author = {M.~Sulzmann and K.~Lu},
+ booktitle = {Proc.~of the 12th International Conference on Functional and Logic Programming (FLOPS)},
+ pages = {203--220},
+ series = {LNCS},
+ title = {{POSIX} {R}egular {E}xpression {P}arsing with {D}erivatives},
+ volume = {8475},
+ year = {2014}}
+
+@inproceedings{Sulzmann2014b,
+ author = {M.~Sulzmann and P.~van Steenhoven},
+ booktitle = {Proc.~of the 23rd International Conference on Compiler Construction (CC)},
+ pages = {174--191},
+ series = {LNCS},
+ title = {{A} {F}lexible and {E}fficient {ML} {L}exer {T}ool {B}ased on {E}xtended {R}egular {E}xpression {S}ubmatching},
+ volume = {8409},
+ year = {2014}}
+
+@book{Pierce2015,
+ author = {B.~C.~Pierce and C.~Casinghino and M.~Gaboardi and M.~Greenberg and C.~Hri\c{t}cu and V.~Sj\"{o}berg and B.~Yorgey},
+ note = {\url{http://www.cis.upenn.edu/~bcpierce/sf}},
+ publisher = {Electronic textbook},
+ title = {{S}oftware {F}oundations},
+ year = {2015}}
+
+@misc{Kuklewicz,
+ author = {C.~Kuklewicz},
+ howpublished = {\url{https://wiki.haskell.org/Regex_Posix}},
+ title = {{R}egex {P}osix}}
+
+@article{Vansummeren2006,
+ author = {S.~Vansummeren},
+ journal = {ACM Transactions on Programming Languages and Systems},
+ number = {3},
+ pages = {389--428},
+ title = {{T}ype {I}nference for {U}nique {P}attern {M}atching},
+ volume = {28},
+ year = {2006}}
+
+@inproceedings{Asperti12,
+ author = {A.~Asperti},
+ booktitle = {Proc.~of the 3rd International Conference on Interactive Theorem Proving (ITP)},
+ pages = {283--298},
+ series = {LNCS},
+ title = {{A} {C}ompact {P}roof of {D}ecidability for {R}egular {E}xpression {E}quivalence},
+ volume = {7406},
+ year = {2012}}
+
+@inproceedings{Frisch2004,
+ author = {A.~Frisch and L.~Cardelli},
+ booktitle = {Proc.~of the 31st International Conference on Automata, Languages and Programming (ICALP)},
+ pages = {618--629},
+ series = {LNCS},
+ title = {{G}reedy {R}egular {E}xpression {M}atching},
+ volume = {3142},
+ year = {2004}}
+
+@article{Antimirov95,
+ author = {V.~Antimirov},
+ journal = {Theoretical Computer Science},
+ pages = {291--319},
+ title = {{P}artial {D}erivatives of {R}egular {E}xpressions and {F}inite {A}utomata {C}onstructions},
+ volume = {155},
+ year = {1995}}
+
+@inproceedings{Nipkow98,
+ author = {T.~Nipkow},
+ booktitle = {Proc.~of the 11th International Conference on Theorem Proving in Higher Order Logics (TPHOLs)},
+ pages = {1--15},
+ series = {LNCS},
+ title = {{V}erified {L}exical {A}nalysis},
+ volume = 1479,
+ year = 1998}
+
+@article{Brzozowski1964,
+ author = {J.~A.~Brzozowski},
+ journal = {Journal of the {ACM}},
+ number = {4},
+ pages = {481--494},
+ title = {{D}erivatives of {R}egular {E}xpressions},
+ volume = {11},
+ year = {1964}}
+
+@article{Leroy2009,
+ author = {X.~Leroy},
+ journal = {Communications of the ACM},
+ number = 7,
+ pages = {107--115},
+ title = {{F}ormal {V}erification of a {R}ealistic {C}ompiler},
+ volume = 52,
+ year = 2009}
+
+@inproceedings{Paulson2015,
+ author = {L.~C.~Paulson},
+ booktitle = {Proc.~of the 25th International Conference on Automated Deduction (CADE)},
+ pages = {231--245},
+ series = {LNAI},
+ title = {{A} {F}ormalisation of {F}inite {A}utomata {U}sing {H}ereditarily {F}inite {S}ets},
+ volume = {9195},
+ year = {2015}}
+
+@article{Wu2014,
+ author = {C.~Wu and X.~Zhang and C.~Urban},
+ journal = {Journal of Automatic Reasoning},
+ number = {4},
+ pages = {451--480},
+ title = {{A} {F}ormalisation of the {M}yhill-{N}erode {T}heorem based on {R}egular {E}xpressions},
+ volume = {52},
+ year = {2014}}
+
+@inproceedings{Regehr2011,
+ author = {X.~Yang and Y.~Chen and E.~Eide and J.~Regehr},
+ booktitle = {Proc.~of the 32nd ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI)},
+ pages = {283--294},
+ title = {{F}inding and {U}nderstanding {B}ugs in {C} {C}ompilers},
+ year = {2011}}
+
+@article{Norrish2014,
+ author = {A.~Barthwal and M.~Norrish},
+ journal = {Journal of Computer and System Sciences},
+ number = {2},
+ pages = {346--362},
+ title = {{A} {M}echanisation of {S}ome {C}ontext-{F}ree {L}anguage {T}heory in {HOL4}},
+ volume = {80},
+ year = {2014}}
+
+@article{Thompson1968,
+ author = {K.~Thompson},
+ issue_date = {June 1968},
+ journal = {Communications of the ACM},
+ number = {6},
+ pages = {419--422},
+ title = {{P}rogramming {T}echniques: {R}egular {E}xpression {S}earch {A}lgorithm},
+ volume = {11},
+ year = {1968}}
+
+@article{Owens2009,
+ author = {S.~Owens and J.~H.~Reppy and A.~Turon},
+ journal = {Journal of Functinal Programming},
+ number = {2},
+ pages = {173--190},
+ title = {{R}egular-{E}xpression {D}erivatives {R}e-{E}xamined},
+ volume = {19},
+ year = {2009}}
+
+@inproceedings{Sulzmann2015,
+ author = {M.~Sulzmann and P.~Thiemann},
+ booktitle = {Proc.~of the 9th International Conference on Language and Automata Theory and Applications (LATA)},
+ pages = {275--286},
+ series = {LNCS},
+ title = {{D}erivatives for {R}egular {S}huffle {E}xpressions},
+ volume = {8977},
+ year = {2015}}
+
+@inproceedings{Chen2012,
+ author = {H.~Chen and S.~Yu},
+ booktitle = {Proc.~in the International Workshop on Theoretical Computer Science (WTCS)},
+ pages = {343--356},
+ series = {LNCS},
+ title = {{D}erivatives of {R}egular {E}xpressions and an {A}pplication},
+ volume = {7160},
+ year = {2012}}
+
+@article{Krauss2011,
+ author = {A.~Krauss and T.~Nipkow},
+ journal = {Journal of Automated Reasoning},
+ pages = {95--106},
+ title = {{P}roof {P}earl: {R}egular {E}xpression {E}quivalence and {R}elation {A}lgebra},
+ volume = 49,
+ year = 2012}
+
+@inproceedings{Traytel2015,
+ author = {D.~Traytel},
+ booktitle = {Proc.~of the 24th Annual Conference on Computer Science Logic (CSL)},
+ pages = {487--503},
+ series = {LIPIcs},
+ title = {{A} {C}oalgebraic {D}ecision {P}rocedure for {WS1S}},
+ volume = {41},
+ year = {2015}}
+
+@inproceedings{Traytel2013,
+ author = {D.~Traytel and T.~Nipkow},
+ booktitle = {Proc.~of the 18th ACM SIGPLAN International Conference on Functional Programming (ICFP)},
+ pages = {3-12},
+ title = {{A} {V}erified {D}ecision {P}rocedure for {MSO} on {W}ords {B}ased on {D}erivatives of {R}egular {E}xpressions},
+ year = 2013}
+
+@inproceedings{Coquand2012,
+ author = {T.~Coquand and V.~Siles},
+ booktitle = {Proc.~of the 1st International Conference on Certified Programs and Proofs (CPP)},
+ pages = {119--134},
+ series = {LNCS},
+ title = {{A} {D}ecision {P}rocedure for {R}egular {E}xpression {E}quivalence in {T}ype {T}heory},
+ volume = {7086},
+ year = {2011}}
+
+@inproceedings{Almeidaetal10,
+ author = {J.~B.~Almeida and N.~Moriera and D.~Pereira and S.~M.~de Sousa},
+ booktitle = {Proc.~of the 15th International Conference on Implementation and Application of Automata (CIAA)},
+ pages = {59-68},
+ series = {LNCS},
+ title = {{P}artial {D}erivative {A}utomata {F}ormalized in {C}oq},
+ volume = {6482},
+ year = {2010}}
+
+@article{Owens2008,
+ author = {S.~Owens and K.~Slind},
+ journal = {Higher-Order and Symbolic Computation},
+ number = {4},
+ pages = {377--409},
+ title = {{A}dapting {F}unctional {P}rograms to {H}igher {O}rder {L}ogic},
+ volume = {21},
+ year = {2008}}
+
+@article{Owens2,
+ author = {S.~Owens and K.~Slind},
+ bibsource = {dblp computer science bibliography, http://dblp.org},
+ biburl = {http://dblp.uni-trier.de/rec/bib/journals/lisp/OwensS08},
+ doi = {10.1007/s10990-008-9038-0},
+ journal = {Higher-Order and Symbolic Computation},
+ number = {4},
+ pages = {377--409},
+ timestamp = {Wed, 16 Dec 2009 13:51:02 +0100},
+ title = {Adapting functional programs to higher order logic},
+ url = {http://dx.doi.org/10.1007/s10990-008-9038-0},
+ volume = {21},
+ year = {2008},
+ bdsk-url-1 = {http://dx.doi.org/10.1007/s10990-008-9038-0}}
+
+@misc{PCRE,
+ title = {{PCRE - Perl Compatible Regular Expressions}},
+ url = {http://www.pcre.org},
+ bdsk-url-1 = {http://www.pcre.org}}
+
+@inproceedings{OkuiSuzuki2010,
+ author = {S.~Okui and T.~Suzuki},
+ booktitle = {Proc.~of the 15th International Conference on Implementation and Application of Automata (CIAA)},
+ pages = {231--240},
+ series = {LNCS},
+ title = {{D}isambiguation in {R}egular {E}xpression {M}atching via {P}osition {A}utomata with {A}ugmented {T}ransitions},
+ volume = {6482},
+ year = {2010}}
+
+@techreport{OkuiSuzukiTech,
+ author = {S.~Okui and T.~Suzuki},
+ institution = {University of Aizu},
+ title = {{D}isambiguation in {R}egular {E}xpression {M}atching via {P}osition {A}utomata with {A}ugmented {T}ransitions},
+ year = {2013}}
+
+@inproceedings{Davis18,
+ author = {J.~C.~Davis and C.~.A.~Coghlan and F.~Servant and D.~Lee},
+ booktitle = {Proc.~of the 26th ACM Joint Meeting on European Software Engineering Conference and Symposium on the Foundations of Software Engineering (ESEC/FSE)},
+ numpages = {11},
+ pages = {246--256},
+ title = {{T}he {I}mpact of {R}egular {E}xpression {D}enial of {S}ervice ({ReDoS}) in {P}ractice: {A}n {E}mpirical {S}tudy at the {E}cosystem {S}cale},
+ year = {2018}}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/exampletemplate.bib Sun Mar 20 23:32:08 2022 +0000
@@ -0,0 +1,40 @@
+@article{Reference1,
+ Abstract = {We have developed an enhanced Littrow configuration extended cavity diode laser (ECDL) that can be tuned without changing the direction of the output beam. The output of a conventional Littrow ECDL is reflected from a plane mirror fixed parallel to the tuning diffraction grating. Using a free-space Michelson wavemeter to measure the laser wavelength, we can tune the laser over a range greater than 10 nm without any alteration of alignment.},
+ Author = {C. J. Hawthorn and K. P. Weber and R. E. Scholten},
+ Journal = {Review of Scientific Instruments},
+ Month = {12},
+ Number = {12},
+ Numpages = {3},
+ Pages = {4477--4479},
+ Title = {Littrow Configuration Tunable External Cavity Diode Laser with Fixed Direction Output Beam},
+ Volume = {72},
+ Url = {http://link.aip.org/link/?RSI/72/4477/1},
+ Year = {2001}}
+
+@article{Reference3,
+ Abstract = {Operating a laser diode in an extended cavity which provides frequency-selective feedback is a very effective method of reducing the laser's linewidth and improving its tunability. We have developed an extremely simple laser of this type, built from inexpensive commercial components with only a few minor modifications. A 780~nm laser built to this design has an output power of 80~mW, a linewidth of 350~kHz, and it has been continuously locked to a Doppler-free rubidium transition for several days.},
+ Author = {A. S. Arnold and J. S. Wilson and M. G. Boshier and J. Smith},
+ Journal = {Review of Scientific Instruments},
+ Month = {3},
+ Number = {3},
+ Numpages = {4},
+ Pages = {1236--1239},
+ Title = {A Simple Extended-Cavity Diode Laser},
+ Volume = {69},
+ Url = {http://link.aip.org/link/?RSI/69/1236/1},
+ Year = {1998}}
+
+@article{Reference2,
+ Abstract = {We present a review of the use of diode lasers in atomic physics with an extensive list of references. We discuss the relevant characteristics of diode lasers and explain how to purchase and use them. We also review the various techniques that have been used to control and narrow the spectral outputs of diode lasers. Finally we present a number of examples illustrating the use of diode lasers in atomic physics experiments. Review of Scientific Instruments is copyrighted by The American Institute of Physics.},
+ Author = {Carl E. Wieman and Leo Hollberg},
+ Journal = {Review of Scientific Instruments},
+ Keywords = {Diode Laser},
+ Month = {1},
+ Number = {1},
+ Numpages = {20},
+ Pages = {1--20},
+ Title = {Using Diode Lasers for Atomic Physics},
+ Volume = {62},
+ Url = {http://link.aip.org/link/?RSI/62/1/1},
+ Year = {1991}}
+
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/good-java.data Sun Mar 20 23:32:08 2022 +0000
@@ -0,0 +1,34 @@
+%% LaTeX2e file `good-java.data'
+%% generated by the `filecontents' environment
+%% from source `main' on 2022/03/16.
+%%
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+2 1.299E-5
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+10 2.8729E-5
+11 3.5367E-5
+12 3.701E-5
+13 3.84E-5
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+16 5.3597E-5
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+27 7.5628E-5
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+30 9.8494E-5
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/graphic.sty Sun Mar 20 23:32:08 2022 +0000
@@ -0,0 +1,12 @@
+\usepackage{tikz}
+%\usepackage{pgf}
+%\usetikzlibrary{positioning}
+%\usetikzlibrary{calc}
+%\usetikzlibrary{automata}
+%\usetikzlibrary{arrows}
+%\usetikzlibrary{backgrounds}
+%\usetikzlibrary{fit}
+%\usepackage{tikz-qtree}
+\usepackage{pgfplots}
+
+%\pgfplotsset{compat=1.15}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/main-blx.bib Sun Mar 20 23:32:08 2022 +0000
@@ -0,0 +1,11 @@
+@Comment{$ biblatex control file $}
+@Comment{$ biblatex version 2.9 $}
+Do not modify this file!
+
+This is an auxiliary file used by the 'biblatex' package.
+This file may safely be deleted. It will be recreated as
+required.
+
+@Control{biblatex-control,
+ options = {2.9:0:0:1:0:1:1:0:0:1:0:2:3:1:79:+:nyt},
+}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/main.aux Sun Mar 20 23:32:08 2022 +0000
@@ -0,0 +1,102 @@
+\relax
+\providecommand\hyper@newdestlabel[2]{}
+\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
+\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
+\global\let\oldcontentsline\contentsline
+\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
+\global\let\oldnewlabel\newlabel
+\gdef\newlabel#1#2{\newlabelxx{#1}#2}
+\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
+\AtEndDocument{\ifx\hyper@anchor\@undefined
+\let\contentsline\oldcontentsline
+\let\newlabel\oldnewlabel
+\fi}
+\fi}
+\global\let\hyper@last\relax
+\gdef\HyperFirstAtBeginDocument#1{#1}
+\providecommand\HyField@AuxAddToFields[1]{}
+\providecommand\HyField@AuxAddToCoFields[2]{}
+\bibstyle{biblatex}
+\bibdata{main-blx,example}
+\citation{biblatex-control}
+\abx@aux@refcontext{nyt/global//global/global}
+\@writefile{toc}{\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax }
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+ \field{title}{{D}erivatives of {R}egular {E}xpressions}
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+ \field{booktitle}{Proc.~of the 1st International Conference on Certified
+ Programs and Proofs (CPP)}
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+ \field{series}{LNCS}
+ \field{title}{{A} {D}ecision {P}rocedure for {R}egular {E}xpression
+ {E}quivalence in {T}ype {T}heory}
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+ \field{year}{2011}
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+ \field{pages}{95\bibrangedash 106}
+ \field{title}{{P}roof {P}earl: {R}egular {E}xpression {E}quivalence and
+ {R}elation {A}lgebra}
+ \field{volume}{49}
+ \field{journaltitle}{Journal of Automated Reasoning}
+ \field{year}{2012}
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+ \field{number}{4}
+ \field{pages}{377\bibrangedash 409}
+ \field{title}{{A}dapting {F}unctional {P}rograms to {H}igher {O}rder
+ {L}ogic}
+ \field{volume}{21}
+ \field{journaltitle}{Higher-Order and Symbolic Computation}
+ \field{year}{2008}
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+ \list{publisher}{1}{%
+ {Association for Computing Machinery}%
+ }
+ \keyw{Certified algorithms, regular expressions, dependent types,
+ bit-codes}
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+ \strng{fullhash}{RRBAD1}
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+ \field{labeltitlesource}{title}
+ \field{labelyear}{2017}
+ \field{labeldatesource}{year}
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+ \field{sortinithash}{R}
+ \field{abstract}{%
+ We describe the formalization of a regular expression (RE) parsing
+ algorithm that produces a bit representation of its parse tree in the
+ dependently typed language Agda. The algorithm computes bit-codes using
+ Brzozowski derivatives and we prove that produced codes are equivalent to
+ parse trees ensuring soundness and completeness w.r.t an inductive RE
+ semantics. We include the certified algorithm in a tool developed by us,
+ named verigrep, for regular expression based search in the style of the well
+ known GNU grep. Practical experiments conducted with this tool are reported.%
+ }
+ \field{booktitle}{Proceedings of the 21st Brazilian Symposium on
+ Programming Languages}
+ \verb{doi}
+ \verb 10.1145/3125374.3125381
+ \endverb
+ \field{isbn}{9781450353892}
+ \field{series}{SBLP 2017}
+ \field{title}{Certified Bit-Coded Regular Expression Parsing}
+ \verb{url}
+ \verb https://doi.org/10.1145/3125374.3125381
+ \endverb
+ \list{location}{1}{%
+ {Fortaleza, CE, Brazil}%
+ }
+ \field{year}{2017}
+ \warn{\item Can't use 'location' + 'address'}
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+\BOOKMARK [1][-]{section.39}{\376\377\000S\000e\000c\000t\000i\000o\000n\000i\000n\000g\000\040\000a\000n\000d\000\040\000S\000u\000b\000s\000e\000c\000t\000i\000o\000n\000i\000n\000g}{chapter.14}% 25
+\BOOKMARK [1][-]{section.40}{\376\377\000I\000n\000\040\000C\000l\000o\000s\000i\000n\000g}{chapter.14}% 26
+\BOOKMARK [0][-]{chapter.41}{\376\377\000C\000h\000a\000p\000t\000e\000r\000\040\000T\000i\000t\000l\000e\000\040\000H\000e\000r\000e}{}% 27
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+\BOOKMARK [2][-]{subsection.43}{\376\377\000f\000u\000n\000c\000t\000i\000o\000n\000\040\000"\0000\0002\0006\000E\0003\0000\000F\000\040\000c\000\040\000i\000s\000\040\000n\000o\000t\000\040\0001\000-\000t\000o\000-\0001}{section.42}% 29
+\BOOKMARK [2][-]{subsection.44}{\376\377\000S\000u\000b\000s\000e\000c\000t\000i\000o\000n\000\040\0001}{section.42}% 30
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+\BOOKMARK [1][-]{section.46}{\376\377\000M\000a\000i\000n\000\040\000S\000e\000c\000t\000i\000o\000n\000\040\0002}{chapter.41}% 32
+\BOOKMARK [0][-]{chapter.47}{\376\377\000C\000o\000m\000m\000o\000n\000\040\000I\000d\000e\000n\000t\000i\000t\000i\000e\000s\000\040\000I\000n\000\040\000S\000i\000m\000p\000l\000i\000f\000i\000c\000a\000t\000i\000o\000n\000-\000R\000e\000l\000a\000t\000e\000d\000\040\000F\000u\000n\000c\000t\000i\000o\000n\000s}{}% 33
+\BOOKMARK [1][-]{section.48}{\376\377\000I\000d\000e\000m\000p\000o\000t\000e\000n\000c\000y\000\040\000o\000f\000\040\000s\000i\000m\000p}{chapter.47}% 34
+\BOOKMARK [2][-]{subsection.50}{\376\377\000S\000y\000n\000t\000a\000c\000t\000i\000c\000\040\000E\000q\000u\000i\000v\000a\000l\000e\000n\000c\000e\000\040\000U\000n\000d\000e\000r\000\040\000s\000i\000m\000p}{section.48}% 35
+\BOOKMARK [2][-]{subsection.51}{\376\377\000S\000u\000b\000s\000e\000c\000t\000i\000o\000n\000\040\0002}{section.48}% 36
+\BOOKMARK [1][-]{section.52}{\376\377\000M\000a\000i\000n\000\040\000S\000e\000c\000t\000i\000o\000n\000\040\0002}{chapter.47}% 37
+\BOOKMARK [0][-]{appendix.53}{\376\377\000F\000r\000e\000q\000u\000e\000n\000t\000l\000y\000\040\000A\000s\000k\000e\000d\000\040\000Q\000u\000e\000s\000t\000i\000o\000n\000s}{}% 38
+\BOOKMARK [1][-]{section.54}{\376\377\000H\000o\000w\000\040\000d\000o\000\040\000I\000\040\000c\000h\000a\000n\000g\000e\000\040\000t\000h\000e\000\040\000c\000o\000l\000o\000r\000s\000\040\000o\000f\000\040\000l\000i\000n\000k\000s\000?}{appendix.53}% 39
+\BOOKMARK [0][-]{appendix*.55}{\376\377\000B\000i\000b\000l\000i\000o\000g\000r\000a\000p\000h\000y}{}% 40
Binary file PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/main.pdf has changed
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/main.run.xml Sun Mar 20 23:32:08 2022 +0000
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+<?xml version="1.0" standalone="yes"?>
+<!-- logreq request file -->
+<!-- logreq version 1.0 / dtd version 1.0 -->
+<!-- Do not edit this file! -->
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+ <!ELEMENT requests (internal | external)*>
+ <!ELEMENT internal (generic, (provides | requires)*)>
+ <!ELEMENT external (generic, cmdline?, input?, output?, (provides | requires)*)>
+ <!ELEMENT cmdline (binary, (option | infile | outfile)*)>
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+ <!ELEMENT generic (#PCDATA)>
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+ version CDATA #REQUIRED
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+ priority (9) #REQUIRED
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+ priority (1 | 2 | 3 | 4 | 5 | 6 | 7 | 8) #REQUIRED
+ active (0 | 1) #REQUIRED
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+ <!ATTLIST provides
+ type (static | dynamic | editable) #REQUIRED
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+ <!ATTLIST requires
+ type (static | dynamic | editable) #REQUIRED
+ >
+ <!ATTLIST file
+ type CDATA #IMPLIED
+ >
+]>
+<requests version="1.0">
+ <internal package="biblatex" priority="9" active="1">
+ <generic>latex</generic>
+ <provides type="dynamic">
+ <file>main.aux</file>
+ <file>main-blx.bib</file>
+ </provides>
+ <requires type="dynamic">
+ <file>main.bbl</file>
+ </requires>
+ <requires type="static">
+ <file>blx-dm.def</file>
+ <file>blx-compat.def</file>
+ <file>blx-bibtex.def</file>
+ <file>biblatex.def</file>
+ <file>blx-natbib.def</file>
+ <file>standard.bbx</file>
+ <file>authoryear.bbx</file>
+ <file>authoryear.cbx</file>
+ <file>biblatex.cfg</file>
+ <file>english.lbx</file>
+ </requires>
+ </internal>
+ <external package="biblatex" priority="5" active="1">
+ <generic>bibtex</generic>
+ <cmdline>
+ <binary>bibtex</binary>
+ <option>-min-crossrefs 2</option>
+ <infile>main</infile>
+ </cmdline>
+ <input>
+ <file>main.aux</file>
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Binary file PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/main.synctex.gz has changed
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/main.tex Sun Mar 20 23:32:08 2022 +0000
@@ -0,0 +1,356 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Masters/Doctoral Thesis
+% LaTeX Template
+% Version 2.5 (27/8/17)
+%
+% This template was downloaded from:
+% http://www.LaTeXTemplates.com
+%
+% Version 2.x major modifications by:
+% Vel (vel@latextemplates.com)
+%
+% This template is based on a template by:
+% Steve Gunn (http://users.ecs.soton.ac.uk/srg/softwaretools/document/templates/)
+% Sunil Patel (http://www.sunilpatel.co.uk/thesis-template/)
+%
+% Template license:
+% CC BY-NC-SA 3.0 (http://creativecommons.org/licenses/by-nc-sa/3.0/)
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%----------------------------------------------------------------------------------------
+% PACKAGES AND OTHER DOCUMENT CONFIGURATIONS
+%----------------------------------------------------------------------------------------
+
+\documentclass[
+11pt, % The default document font size, options: 10pt, 11pt, 12pt
+%oneside, % Two side (alternating margins) for binding by default, uncomment to switch to one side
+english, % ngerman for German
+singlespacing, % Single line spacing, alternatives: onehalfspacing or doublespacing
+%draft, % Uncomment to enable draft mode (no pictures, no links, overfull hboxes indicated)
+%nolistspacing, % If the document is onehalfspacing or doublespacing, uncomment this to set spacing in lists to single
+%liststotoc, % Uncomment to add the list of figures/tables/etc to the table of contents
+%toctotoc, % Uncomment to add the main table of contents to the table of contents
+%parskip, % Uncomment to add space between paragraphs
+%nohyperref, % Uncomment to not load the hyperref package
+headsepline, % Uncomment to get a line under the header
+%chapterinoneline, % Uncomment to place the chapter title next to the number on one line
+%consistentlayout, % Uncomment to change the layout of the declaration, abstract and acknowledgements pages to match the default layout
+]{MastersDoctoralThesis} % The class file specifying the document structure
+
+\usepackage[utf8]{inputenc} % Required for inputting international characters
+\usepackage[T1]{fontenc} % Output font encoding for international characters
+
+\usepackage{mathpazo} % Use the Palatino font by default
+\usepackage{hyperref}
+\usepackage[backend=bibtex,style=authoryear,natbib=true]{biblatex} % Use the bibtex backend with the authoryear citation style (which resembles APA)
+
+\addbibresource{example.bib} % The filename of the bibliography
+
+\usepackage[autostyle=true]{csquotes} % Required to generate language-dependent quotes in the bibliography
+
+%My Newly added Libraries in addition to template
+\usepackage{graphic}
+\usepackage{data}
+
+%\usepackage{algorithm}
+\usepackage{amsmath}
+\usepackage[noend]{algpseudocode}
+\usepackage{enumitem}
+\usepackage{nccmath}
+\usepackage{tikz-cd}
+\usetikzlibrary{positioning}
+
+%----------------------------------------------------------------------------------------
+% MARGIN SETTINGS
+%----------------------------------------------------------------------------------------
+
+\geometry{
+ paper=a4paper, % Change to letterpaper for US letter
+ inner=2.5cm, % Inner margin
+ outer=3.8cm, % Outer margin
+ bindingoffset=.5cm, % Binding offset
+ top=1.5cm, % Top margin
+ bottom=1.5cm, % Bottom margin
+ %showframe, % Uncomment to show how the type block is set on the page
+}
+
+%----------------------------------------------------------------------------------------
+% THESIS INFORMATION
+%----------------------------------------------------------------------------------------
+
+\thesistitle{POSIX Regular Expression Matching and Lexing} % Your thesis title, this is used in the title and abstract, print it elsewhere with \ttitle
+\supervisor{Dr. Christian \textsc{Urban}} % Your supervisor's name, this is used in the title page, print it elsewhere with \supname
+\examiner{} % Your examiner's name, this is not currently used anywhere in the template, print it elsewhere with \examname
+\degree{Doctor of Philosophy} % Your degree name, this is used in the title page and abstract, print it elsewhere with \degreename
+\author{Chengsong \textsc{Tan}} % Your name, this is used in the title page and abstract, print it elsewhere with \authorname
+\addresses{} % Your address, this is not currently used anywhere in the template, print it elsewhere with \addressname
+
+\subject{Computer Science} % Your subject area, this is not currently used anywhere in the template, print it elsewhere with \subjectname
+\keywords{} % Keywords for your thesis, this is not currently used anywhere in the template, print it elsewhere with \keywordnames
+\university{\href{https://www.kcl.ac.uk}{King's College London}} % Your university's name and URL, this is used in the title page and abstract, print it elsewhere with \univname
+\department{\href{https://www.kcl.ac.uk/informatics}{Department or Informatics}} % Your department's name and URL, this is used in the title page and abstract, print it elsewhere with \deptname
+\group{\href{https://www.kcl.ac.uk/research/ssy}{Software Systems}} % Your research group's name and URL, this is used in the title page, print it elsewhere with \groupname
+\faculty{\href{http://faculty.university.com}{Chengsong Tan}} % Your faculty's name and URL, this is used in the title page and abstract, print it elsewhere with \facname
+
+\AtBeginDocument{
+\hypersetup{pdftitle=\ttitle} % Set the PDF's title to your title
+\hypersetup{pdfauthor=\authorname} % Set the PDF's author to your name
+\hypersetup{pdfkeywords=\keywordnames} % Set the PDF's keywords to your keywords
+}
+
+\begin{document}
+
+\frontmatter % Use roman page numbering style (i, ii, iii, iv...) for the pre-content pages
+
+\pagestyle{plain} % Default to the plain heading style until the thesis style is called for the body content
+
+%----------------------------------------------------------------------------------------
+% TITLE PAGE
+%----------------------------------------------------------------------------------------
+
+\begin{titlepage}
+\begin{center}
+
+\vspace*{.06\textheight}
+{\scshape\LARGE \univname\par}\vspace{1.5cm} % University name
+\textsc{\Large Doctoral Thesis}\\[0.5cm] % Thesis type
+
+\HRule \\[0.4cm] % Horizontal line
+{\huge \bfseries \ttitle\par}\vspace{0.4cm} % Thesis title
+\HRule \\[1.5cm] % Horizontal line
+
+\begin{minipage}[t]{0.4\textwidth}
+\begin{flushleft} \large
+\emph{Author:}\\
+\href{https://kclpure.kcl.ac.uk/portal/en/persons/chengsong-tan(a63b381b-04bc-4cd7-beea-beb3e96cb153).html}{\authorname} % Author name - remove the \href bracket to remove the link
+\end{flushleft}
+\end{minipage}
+
+
+\begin{minipage}[t]{0.4\textwidth}
+\begin{flushright} \large
+\emph{Supervisor:} \\
+\href{https://www.kcl.ac.uk/people/christian-urban}{\supname} % Supervisor name - remove the \href bracket to remove the link
+\end{flushright}
+\end{minipage}\\[3cm]
+
+\vfill
+
+\large \textit{A thesis submitted in fulfillment of the requirements\\ for the degree of \degreename}\\[0.3cm] % University requirement text
+\textit{in the}\\[0.4cm]
+\groupname\\\deptname\\[2cm] % Research group name and department name
+
+\vfill
+
+{\large \today}\\[4cm] % Date
+%\includegraphics{Logo} % University/department logo - uncomment to place it
+
+\vfill
+\end{center}
+\end{titlepage}
+
+%----------------------------------------------------------------------------------------
+% DECLARATION PAGE
+%----------------------------------------------------------------------------------------
+
+\begin{declaration}
+\addchaptertocentry{\authorshipname} % Add the declaration to the table of contents
+\noindent I, \authorname, declare that this thesis titled, \enquote{\ttitle} and the work presented in it are my own. I confirm that:
+
+\begin{itemize}
+\item This work was done wholly or mainly while in candidature for a research degree at this University.
+\item Where any part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution, this has been clearly stated.
+\item Where I have consulted the published work of others, this is always clearly attributed.
+\item Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work.
+\item I have acknowledged all main sources of help.
+\item Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself.\\
+\end{itemize}
+
+\noindent Signed:\\
+\rule[0.5em]{25em}{0.5pt} % This prints a line for the signature
+
+\noindent Date:\\
+\rule[0.5em]{25em}{0.5pt} % This prints a line to write the date
+\end{declaration}
+
+\cleardoublepage
+
+%----------------------------------------------------------------------------------------
+% QUOTATION PAGE
+%----------------------------------------------------------------------------------------
+
+\vspace*{0.2\textheight}
+
+\noindent\enquote{\itshape Thanks to my solid academic training, today I can write hundreds of words on virtually any topic without possessing a shred of information, which is how I got a good job in journalism.}\bigbreak
+
+\hfill Dave Barry
+
+%----------------------------------------------------------------------------------------
+% ABSTRACT PAGE
+%----------------------------------------------------------------------------------------
+
+\begin{abstract}
+\addchaptertocentry{\abstractname} % Add the abstract to the table of contents
+This work is a combination of functional algorithms
+and formal methods.
+Regular expression matching and lexing has been
+ widely-used and well-implemented
+in software industry.
+
+Theoretical results say that regular expression matching
+should be linear with respect to the input.
+Under a certain class of regular expressions and inputs though,
+practical implementations suffer from non-linear or even
+exponential running time,
+allowing a ReDoS (regular expression denial-of-service ) attack.
+
+
+The reason behind is that regex libraries in popular language engines
+ often want to support richer constructs
+than the most basic regular expressions, and lexing rather than matching
+is needed for sub-match extraction.
+
+This work aims to address the above vulnerability by the combination
+of Brzozowski's derivatives and interactive theorem proving. We give an
+improved version of Sulzmann and Lu's bit-coded algorithm using
+derivatives, which come with a formal guarantee in terms of correctness and
+running time as an Isabelle/HOL proof.
+Then we improve the algorithm with an even stronger version of
+simplification, and prove a time bound linear to input and
+cubic to regular expression size using a technique by
+Antimirov.
+
+
+
+
+\end{abstract}
+
+%----------------------------------------------------------------------------------------
+% ACKNOWLEDGEMENTS
+%----------------------------------------------------------------------------------------
+
+\begin{acknowledgements}
+\addchaptertocentry{\acknowledgementname} % Add the acknowledgements to the table of contents
+The acknowledgments and the people to thank go here, don't forget to include your project advisor\ldots
+\end{acknowledgements}
+
+%----------------------------------------------------------------------------------------
+% LIST OF CONTENTS/FIGURES/TABLES PAGES
+%----------------------------------------------------------------------------------------
+
+\tableofcontents % Prints the main table of contents
+
+\listoffigures % Prints the list of figures
+
+\listoftables % Prints the list of tables
+
+%----------------------------------------------------------------------------------------
+% ABBREVIATIONS
+%----------------------------------------------------------------------------------------
+
+\begin{abbreviations}{ll} % Include a list of abbreviations (a table of two columns)
+
+\textbf{LAH} & \textbf{L}ist \textbf{A}bbreviations \textbf{H}ere\\
+\textbf{WSF} & \textbf{W}hat (it) \textbf{S}tands \textbf{F}or\\
+
+\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}%
+\newcommand{\ZERO}{\mbox{\bf 0}}
+\newcommand{\ONE}{\mbox{\bf 1}}
+\def\lexer{\mathit{lexer}}
+\def\mkeps{\mathit{mkeps}}
+
+\def\DFA{\textit{DFA}}
+\def\bmkeps{\textit{bmkeps}}
+\def\retrieve{\textit{retrieve}}
+\def\blexer{\textit{blexer}}
+\def\flex{\textit{flex}}
+\def\inj{\mathit{inj}}
+\def\Empty{\mathit{Empty}}
+\def\Left{\mathit{Left}}
+\def\Right{\mathit{Right}}
+\def\Stars{\mathit{Stars}}
+\def\Char{\mathit{Char}}
+\def\Seq{\mathit{Seq}}
+\def\Der{\mathit{Der}}
+\def\nullable{\mathit{nullable}}
+\def\Z{\mathit{Z}}
+\def\S{\mathit{S}}
+\def\rup{r^\uparrow}
+
+\end{abbreviations}
+
+%----------------------------------------------------------------------------------------
+% PHYSICAL CONSTANTS/OTHER DEFINITIONS
+%----------------------------------------------------------------------------------------
+
+\begin{constants}{lr@{${}={}$}l} % The list of physical constants is a three column table
+
+% The \SI{}{} command is provided by the siunitx package, see its documentation for instructions on how to use it
+
+Speed of Light & $c_{0}$ & \SI{2.99792458e8}{\meter\per\second} (exact)\\
+%Constant Name & $Symbol$ & $Constant Value$ with units\\
+
+\end{constants}
+
+%----------------------------------------------------------------------------------------
+% SYMBOLS
+%----------------------------------------------------------------------------------------
+
+\begin{symbols}{lll} % Include a list of Symbols (a three column table)
+
+$a$ & distance & \si{\meter} \\
+$P$ & power & \si{\watt} (\si{\joule\per\second}) \\
+%Symbol & Name & Unit \\
+
+\addlinespace % Gap to separate the Roman symbols from the Greek
+
+$\omega$ & angular frequency & \si{\radian} \\
+
+\end{symbols}
+
+%----------------------------------------------------------------------------------------
+% DEDICATION
+%----------------------------------------------------------------------------------------
+
+\dedicatory{For/Dedicated to/To my\ldots}
+
+%----------------------------------------------------------------------------------------
+% THESIS CONTENT - CHAPTERS
+%----------------------------------------------------------------------------------------
+
+\mainmatter % Begin numeric (1,2,3...) page numbering
+
+\pagestyle{thesis} % Return the page headers back to the "thesis" style
+
+% Include the chapters of the thesis as separate files from the Chapters folder
+% Uncomment the lines as you write the chapters
+
+\include{Chapters/Chapter1}
+\include{Chapters/Chapter2}
+\include{Chapters/Chapter3}
+%\include{Chapters/Chapter4}
+%\include{Chapters/Chapter5}
+
+%----------------------------------------------------------------------------------------
+% THESIS CONTENT - APPENDICES
+%----------------------------------------------------------------------------------------
+
+\appendix % Cue to tell LaTeX that the following "chapters" are Appendices
+
+% Include the appendices of the thesis as separate files from the Appendices folder
+% Uncomment the lines as you write the Appendices
+
+\include{Appendices/AppendixA}
+%\include{Appendices/AppendixB}
+%\include{Appendices/AppendixC}
+
+%----------------------------------------------------------------------------------------
+% BIBLIOGRAPHY
+%----------------------------------------------------------------------------------------
+
+\printbibliography[heading=bibintoc]
+
+%----------------------------------------------------------------------------------------
+
+\end{document}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/main.toc Sun Mar 20 23:32:08 2022 +0000
@@ -0,0 +1,42 @@
+\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax
+\babel@toc {english}{}
+\contentsline {chapter}{Declaration of Authorship}{iii}{section*.1}
+\contentsline {chapter}{Abstract}{vii}{section*.2}
+\contentsline {chapter}{Acknowledgements}{ix}{section*.3}
+\contentsline {chapter}{\numberline {1}Introduction}{1}{chapter.14}
+\contentsline {section}{\numberline {1.1}Why Brzozowski}{2}{section.15}
+\contentsline {section}{\numberline {1.2}Backgound}{4}{section.16}
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+File: tikzlibrarypositioning.code.tex 2008/10/06 v3.0.1a (rcs-revision 1.7)
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Binary file PhdThesisRealOne/automata_view.pdf has changed
Binary file PhdThesisRealOne/automata_view.synctex.gz has changed
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/PhdThesisRealOne/automata_view.tex Sun Mar 20 23:32:08 2022 +0000
@@ -0,0 +1,20 @@
+\documentclass{article}
+
+\usepackage{tikz}
+\usetikzlibrary{automata,positioning}
+\begin{document}
+\section{regular expression derivatives as NFA's}
+\begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid,auto]
+ \node[state,initial] (q_0) {$q_0$};
+ \node[state] (q_1) [above right=of q_0] {$q_1$};
+ \node[state] (q_2) [below right=of q_0] {$q_2$};
+ \node[state,accepting](q_3) [below right=of q_1] {$q_3$};
+ \path[->]
+ (q_0) edge node {0} (q_1)
+ edge node [swap] {1} (q_2)
+ (q_1) edge node {1} (q_3)
+ edge [loop above] node {0} ()
+ (q_2) edge node [swap] {0} (q_3)
+ edge [loop below] node {1} ();
+\end{tikzpicture}
+\end{document}
\ No newline at end of file
Binary file PhdThesisRealOne/thesis.pdf has changed
--- a/thys2/ClosedForms.thy Sat Mar 19 10:36:52 2022 +0000
+++ b/thys2/ClosedForms.thy Sun Mar 20 23:32:08 2022 +0000
@@ -7,6 +7,52 @@
sorry
+
+
+lemma distinct_removes_last:
+ shows "\<lbrakk>(a::rrexp) \<in> set as\<rbrakk>
+ \<Longrightarrow> rdistinct as rset = rdistinct (as @ [a]) rset"
+and "rdistinct (ab # as @ [ab]) rset1 = rdistinct (ab # as) rset1"
+ apply(induct as arbitrary: rset ab rset1 a)
+ apply simp
+ apply simp
+ apply(case_tac "aa \<in> rset")
+ apply(case_tac "a = aa")
+ apply (metis append_Cons)
+ apply simp
+ apply(case_tac "a \<in> set as")
+ apply (metis append_Cons rdistinct.simps(2) set_ConsD)
+ apply(case_tac "a = aa")
+ prefer 2
+ apply simp
+ apply (metis append_Cons)
+ apply(case_tac "ab \<in> rset1")
+ prefer 2
+ apply(subgoal_tac "rdistinct (ab # (a # as) @ [ab]) rset1 =
+ ab # (rdistinct ((a # as) @ [ab]) (insert ab rset1))")
+ prefer 2
+ apply force
+ apply(simp only:)
+ apply(subgoal_tac "rdistinct (ab # a # as) rset1 = ab # (rdistinct (a # as) (insert ab rset1))")
+ apply(simp only:)
+ apply(subgoal_tac "rdistinct ((a # as) @ [ab]) (insert ab rset1) = rdistinct (a # as) (insert ab rset1)")
+ apply blast
+ apply(case_tac "a \<in> insert ab rset1")
+ apply simp
+ apply (metis insertI1)
+ apply simp
+ apply (meson insertI1)
+ apply simp
+ apply(subgoal_tac "rdistinct ((a # as) @ [ab]) rset1 = rdistinct (a # as) rset1")
+ apply simp
+ by (metis append_Cons insert_iff insert_is_Un rdistinct.simps(2))
+
+
+lemma distinct_removes_last2:
+ shows "\<lbrakk>(a::rrexp) \<in> set as\<rbrakk>
+ \<Longrightarrow> rdistinct as rset = rdistinct (as @ [a]) rset"
+ using distinct_removes_last(1) by presburger
+
lemma distinct_append_simp:
shows " rsimp (rsimp_ALTs rs1) = rsimp (rsimp_ALTs rs2) \<Longrightarrow>
rsimp (rsimp_ALTs (f a # rs1)) =
@@ -84,10 +130,8 @@
shows " RONE = rder xa r2 \<Longrightarrow> r2 = RCHAR xa"
apply(case_tac r2)
apply simp+
-
using rrexp.distinct(1) apply presburger
apply (metis rder.simps(5) rrexp.distinct(13) rrexp.simps(20))
-
apply simp+
done
@@ -134,93 +178,8 @@
apply simp
done
-
-lemma alts_preimage_cases:
- shows "rder x r = RALT (RSEQ r1 r2) r3 \<Longrightarrow> (\<exists>ra rb. r = RSEQ ra rb) \<or> (\<exists>rc rd re. r = RALT (RSEQ rc rd) re)"
- apply(case_tac r)
- apply simp+
-
- apply (metis rrexp.simps(12) rrexp.simps(20))
- prefer 3
- apply simp
- apply blast
- apply(frule alts_preimage_case2_2)
- apply(case_tac "(\<exists>ra rb. r = RSEQ ra rb)")
- apply blast
- apply(subgoal_tac " (\<exists> rc rd. r = RALT rc rd )")
- prefer 2
- apply blast
- apply(erule exE)+
- apply(subgoal_tac "rder x r = RALT (rder x rc) (rder x rd)")
- prefer 2
- apply force
- apply(subgoal_tac "rder x rc = RSEQ r1 r2")
- oops
-
-
-lemma der_seq_eq_case:
- shows "\<lbrakk>r1 \<noteq> r2 ; r1 = RSEQ ra rb; rder x r1 = rder x r2\<rbrakk> \<Longrightarrow> rsimp (rder x r1) = RZERO \<and> rsimp (rder x r2) = RZERO"
- apply(case_tac "rnullable ra")
- apply simp
- oops
-
-
-
-
-lemma der_map_unequal_to_equal_zero_only:
- shows "\<lbrakk>r1 \<noteq> r2 ; rder x r1 = rder x r2 \<rbrakk> \<Longrightarrow> rsimp (rder x r1) = RZERO"
- apply(induct r1)
- apply simp
- apply simp
- apply simp
- apply(case_tac "x = xa")
- apply simp
- apply(subgoal_tac "r2 = RCHAR xa")
- prefer 2
- using inv_one_derx apply blast
- apply simp
- using rsimp.simps(3) apply presburger
- apply(case_tac "rder x (RSEQ r11 r12)")
- apply simp
- apply (metis inv_one_derx)
- apply (metis rrexp.distinct(21) rrexp.simps(24) shape_of_derseq)
- apply(subgoal_tac "rder x r2 = RSEQ x41 x42")
- prefer 2
- apply presburger
- apply(subgoal_tac "x41 = rder x r11")
- prefer 2
- apply (meson shape_of_derseq2)
- apply(case_tac r2)
- apply simp+
- apply (metis rrexp.distinct(13) rrexp.simps(10))
- apply(subgoal_tac "x42a = x42")
- prefer 2
- apply (metis rrexp.inject(2) rrexp.simps(30) shape_of_derseq)
- apply(subgoal_tac "rder x x41a = x41")
- prefer 2
- apply (metis shape_of_derseq2)
- apply(simp)
- apply(subgoal_tac "\<not> rnullable r11")
- prefer 2
- apply force
- apply simp
- apply(subgoal_tac "\<not> rnullable x41a")
- prefer 2
- apply force
- apply simp
-
- oops
-
-
-
-lemma der_maps_1to1_except0:
- shows "\<lbrakk>rder x ` rset = dset; a \<notin> rset; rder x a \<in> dset\<rbrakk> \<Longrightarrow> rsimp (rder x a) = RZERO"
-
-
- sorry
-
lemma distinct_der_set:
shows "(rder x) ` rset = dset \<Longrightarrow>
rsimp (rsimp_ALTs (map (rder x) (rdistinct rs rset))) = rsimp ( rsimp_ALTs (rdistinct (map (rder x) rs) dset))"
@@ -263,19 +222,46 @@
lemma non_empty_list:
shows "a \<in> set as \<Longrightarrow> as \<noteq> []"
-
by (metis empty_iff empty_set)
+lemma distinct_comp:
+ shows "rdistinct (rs1@rs2) {} = (rdistinct rs1 {}) @ (rdistinct rs2 (set rs1))"
+ apply(induct rs2 arbitrary: rs1)
+ apply simp
+ apply(subgoal_tac "rs1 @ a # rs2 = (rs1 @ [a]) @ rs2")
+ apply(simp only:)
+ apply(case_tac "a \<in> set rs1")
+ apply simp
+ oops
-lemma distinct_removes_last:
- shows "\<lbrakk>a \<in> set as; rsimp a \<in> set (map rsimp as)\<rbrakk>
- \<Longrightarrow> rsimp_ALTs (rdistinct (rflts (map rsimp as @ [rsimp a])) {}) =
- rsimp_ALTs (rdistinct (rflts (map rsimp as)) {})"
- apply(induct "rsimp a" arbitrary: as)
- apply(simp)
- apply (metis append.right_neutral append_self_conv2 empty_set list.simps(9) map_append rflts.simps(2) rsimp.simps(2) rsimp_idem simp_more_distinct spawn_simp_rsimpalts)
+lemma instantiate1:
+ shows "\<lbrakk>\<And>ab rset1. rdistinct (ab # as) rset1 = rdistinct (ab # as @ [ab]) rset1\<rbrakk> \<Longrightarrow>
+rdistinct (aa # as) rset = rdistinct (aa # as @ [aa]) rset"
+ apply(drule_tac x = "aa" in meta_spec)
+ apply(drule_tac x = "rset" in meta_spec)
apply simp
- sorry
+ done
+
+
+lemma not_head_elem:
+ shows " \<lbrakk>aa \<in> set (a # as); aa \<notin> (set as)\<rbrakk> \<Longrightarrow> a = aa"
+
+ by fastforce
+
+(*
+ apply simp
+ apply (metis append_Cons)
+ apply(case_tac "ab \<in> rset1")
+ apply (metis (no_types, opaque_lifting) Un_insert_left append_Cons insert_iff rdistinct.simps(2) sup_bot_left)
+ apply(subgoal_tac "rdistinct (ab # (aa # as) @ [ab]) rset1 =
+ ab # (rdistinct ((aa # as) @ [ab]) (insert ab rset1))")
+ apply(simp only:)
+ apply(subgoal_tac "rdistinct (ab # aa # as) rset1 = ab # (rdistinct (aa # as) (insert ab rset1))")
+ apply(simp only:)
+ apply(subgoal_tac "rdistinct ((aa # as) @ [ab]) (insert ab rset1) = rdistinct (aa # as) (insert ab rset1)")
+ apply blast
+*)
+
lemma flts_identity1:
shows "rflts (rs @ [RONE]) = rflts rs @ [RONE] "
@@ -319,7 +305,68 @@
using flts_identity11 apply auto[1]
apply blast
using flts_identity12 by presburger
+
+lemma flts_identity3:
+ shows "a = RZERO \<Longrightarrow> rflts (rs @ [a]) = rflts rs"
+ apply simp
+ apply(induct rs)
+ apply simp+
+ apply(case_tac aa)
+ apply simp+
+ done
+
+lemma distinct_removes_last3:
+ shows "\<lbrakk>(a::rrexp) \<in> set as\<rbrakk>
+ \<Longrightarrow> rdistinct as {} = rdistinct (as @ [a]) {}"
+ using distinct_removes_last2 by blast
+
+lemma set_inclusion_with_flts1:
+ shows " \<lbrakk>RONE \<in> set rs\<rbrakk> \<Longrightarrow> RONE \<in> set (rflts rs)"
+ apply(induct rs)
+ apply simp
+ apply(case_tac " RONE \<in> set rs")
+ apply simp
+ apply (metis Un_upper2 insert_absorb insert_subset list.set_intros(2) rflts.simps(2) rflts.simps(3) rflts_def_idiot set_append)
+ apply(case_tac "RONE = a")
+ apply simp
+ apply simp
+ done
+
+lemma set_inclusion_with_flts10:
+ shows " \<lbrakk>RCHAR x \<in> set rs\<rbrakk> \<Longrightarrow> RCHAR x \<in> set (rflts rs)"
+ apply(induct rs)
+ apply simp
+ apply(case_tac " RCHAR x \<in> set rs")
+ apply simp
+ apply (metis Un_upper2 insert_absorb insert_subset rflts.simps(2) rflts.simps(3) rflts_def_idiot set_append set_subset_Cons)
+ apply(case_tac "RCHAR x = a")
+ apply simp
+ apply fastforce
+ apply simp
+ done
+
+lemma set_inclusion_with_flts11:
+ shows " \<lbrakk>RSEQ r1 r2 \<in> set rs\<rbrakk> \<Longrightarrow> RSEQ r1 r2 \<in> set (rflts rs)"
+ apply(induct rs)
+ apply simp
+ apply(case_tac " RSEQ r1 r2 \<in> set rs")
+ apply simp
+ apply (metis Un_upper2 insert_absorb insert_subset rflts.simps(2) rflts.simps(3) rflts_def_idiot set_append set_subset_Cons)
+ apply(case_tac "RSEQ r1 r2 = a")
+ apply simp
+ apply fastforce
+ apply simp
+ done
+
+
+lemma set_inclusion_with_flts:
+ shows " \<lbrakk>a \<in> set as; rsimp a \<in> set (map rsimp as); rsimp a = RONE\<rbrakk> \<Longrightarrow> rsimp a \<in> set (rflts (map rsimp as))"
+ by (simp add: set_inclusion_with_flts1)
+lemma "\<And>x5. \<lbrakk>a \<in> set as; rsimp a \<in> set (map rsimp as); rsimp a = RALTS x5\<rbrakk>
+ \<Longrightarrow> rsimp_ALTs (rdistinct (rflts (map rsimp as @ [rsimp a])) {}) =
+rsimp_ALTs (rdistinct (rflts (map rsimp as @ x5)) {})"
+
lemma last_elem_dup1:
shows " a \<in> set as \<Longrightarrow> rsimp (RALTS (as @ [a] )) = rsimp (RALTS (as ))"
@@ -327,7 +374,17 @@
apply(subgoal_tac "rsimp a \<in> set (map rsimp as)")
prefer 2
apply simp
-
+ apply(case_tac "rsimp a")
+ apply simp
+
+ using flts_identity3 apply presburger
+ apply(subst flts_identity2)
+ using rrexp.distinct(1) rrexp.distinct(15) apply presburger
+ apply(subst distinct_removes_last3[symmetric])
+ using set_inclusion_with_flts apply blast
+ apply simp
+ apply (metis distinct_removes_last3 flts_identity10 set_inclusion_with_flts10)
+ apply (metis distinct_removes_last3 flts_identity11 set_inclusion_with_flts11)
sorry
lemma last_elem_dup: