--- a/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/main.toc	Wed Mar 23 10:09:32 2022 +0000
+++ b/PhdThesisRealOne/LaTeXTemplates_masters-doctoral-thesis_v2/main.toc	Thu Mar 24 20:52:34 2022 +0000
@@ -3,40 +3,43 @@
 \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}
-\contentsline {section}{\numberline {1.3}Existing Practical Approaches}{5}{section.17}
-\contentsline {subsection}{\numberline {1.3.1}DFA Approach}{5}{subsection.18}
-\contentsline {subsection}{\numberline {1.3.2}NFA Approach}{5}{subsection.19}
-\contentsline {section}{\numberline {1.4}Our Approach}{5}{section.20}
-\contentsline {subsection}{\numberline {1.4.1}Existing Work}{5}{subsection.21}
-\contentsline {section}{\numberline {1.5}What this Template Includes}{5}{section.22}
-\contentsline {subsection}{\numberline {1.5.1}Folders}{5}{subsection.23}
-\contentsline {subsection}{\numberline {1.5.2}Files}{6}{subsection.24}
-\contentsline {section}{\numberline {1.6}Filling in Your Information in the \texttt {\bfseries main.tex} File}{7}{section.25}
-\contentsline {section}{\numberline {1.7}The \texttt {main.tex} File Explained}{7}{section.26}
-\contentsline {section}{\numberline {1.8}Thesis Features and Conventions}{8}{section.27}
-\contentsline {subsection}{\numberline {1.8.1}Printing Format}{8}{subsection.28}
-\contentsline {subsection}{\numberline {1.8.2}Using US Letter Paper}{9}{subsection.29}
-\contentsline {subsection}{\numberline {1.8.3}References}{9}{subsection.30}
-\contentsline {subsubsection}{A Note on bibtex}{9}{section*.32}
-\contentsline {subsection}{\numberline {1.8.4}Tables}{10}{subsection.33}
-\contentsline {subsection}{\numberline {1.8.5}Figures}{10}{subsection.35}
-\contentsline {subsection}{\numberline {1.8.6}Typesetting mathematics}{11}{subsection.37}
-\contentsline {section}{\numberline {1.9}Sectioning and Subsectioning}{12}{section.39}
-\contentsline {section}{\numberline {1.10}In Closing}{12}{section.40}
-\contentsline {chapter}{\numberline {2}Chapter Title Here}{13}{chapter.41}
-\contentsline {section}{\numberline {2.1}Properties of $\delimiter "026E30F c$}{13}{section.42}
-\contentsline {subsection}{\numberline {2.1.1}function $\delimiter "026E30F c$ is not 1-to-1}{13}{subsection.43}
-\contentsline {subsection}{\numberline {2.1.2}Subsection 1}{13}{subsection.44}
-\contentsline {subsection}{\numberline {2.1.3}Subsection 2}{13}{subsection.45}
-\contentsline {section}{\numberline {2.2}Main Section 2}{14}{section.46}
-\contentsline {chapter}{\numberline {3}Common Identities In Simplification-Related Functions}{15}{chapter.47}
-\contentsline {section}{\numberline {3.1}Idempotency of $\mathit {simp}$}{15}{section.48}
-\contentsline {subsection}{\numberline {3.1.1}Syntactic Equivalence Under $\mathit {simp}$}{15}{subsection.50}
-\contentsline {subsection}{\numberline {3.1.2}Subsection 2}{15}{subsection.51}
-\contentsline {section}{\numberline {3.2}Main Section 2}{15}{section.52}
-\contentsline {chapter}{\numberline {A}Frequently Asked Questions}{17}{appendix.53}
-\contentsline {section}{\numberline {A.1}How do I change the colors of links?}{17}{section.54}
-\contentsline {chapter}{Bibliography}{19}{appendix*.55}
+\contentsline {chapter}{\numberline {1}POSIX Lexing With Bit-codes}{1}{chapter.14}
+\contentsline {section}{\numberline {1.1}Introduction To Regexes}{1}{section.15}
+\contentsline {subsection}{\numberline {1.1.1}Back References in Regex--Non-Regular part}{4}{subsection.16}
+\contentsline {section}{\numberline {1.2}Our Solution--Brzozowski Derivatives}{4}{section.17}
+\contentsline {section}{\numberline {1.3}Preliminaries about Lexing Using Brzozowski derivatives}{4}{section.18}
+\contentsline {section}{\numberline {1.4}Backgound}{14}{section.25}
+\contentsline {section}{\numberline {1.5}Engineering and Academic Approaches to Deal with Catastrophic Backtracking}{15}{section.26}
+\contentsline {subsection}{\numberline {1.5.1}DFA Approach}{15}{subsection.27}
+\contentsline {subsection}{\numberline {1.5.2}NFA Approach}{15}{subsection.28}
+\contentsline {section}{\numberline {1.6}Our Approach}{15}{section.29}
+\contentsline {subsection}{\numberline {1.6.1}Existing Work}{15}{subsection.30}
+\contentsline {section}{\numberline {1.7}What this Template Includes}{16}{section.31}
+\contentsline {subsection}{\numberline {1.7.1}Folders}{16}{subsection.32}
+\contentsline {subsection}{\numberline {1.7.2}Files}{16}{subsection.33}
+\contentsline {section}{\numberline {1.8}Filling in Your Information in the \texttt {\bfseries main.tex} File}{17}{section.34}
+\contentsline {section}{\numberline {1.9}The \texttt {main.tex} File Explained}{17}{section.35}
+\contentsline {section}{\numberline {1.10}Thesis Features and Conventions}{18}{section.36}
+\contentsline {subsection}{\numberline {1.10.1}Printing Format}{19}{subsection.37}
+\contentsline {subsection}{\numberline {1.10.2}Using US Letter Paper}{19}{subsection.38}
+\contentsline {subsection}{\numberline {1.10.3}References}{19}{subsection.39}
+\contentsline {subsubsection}{A Note on bibtex}{20}{section*.41}
+\contentsline {subsection}{\numberline {1.10.4}Tables}{20}{subsection.42}
+\contentsline {subsection}{\numberline {1.10.5}Figures}{20}{subsection.44}
+\contentsline {subsection}{\numberline {1.10.6}Typesetting mathematics}{22}{subsection.46}
+\contentsline {section}{\numberline {1.11}Sectioning and Subsectioning}{22}{section.48}
+\contentsline {section}{\numberline {1.12}In Closing}{22}{section.49}
+\contentsline {chapter}{\numberline {2}Chapter Title Here}{23}{chapter.50}
+\contentsline {section}{\numberline {2.1}Properties of $\delimiter "026E30F c$}{23}{section.51}
+\contentsline {subsection}{\numberline {2.1.1}function $\delimiter "026E30F c$ is not 1-to-1}{23}{subsection.52}
+\contentsline {subsection}{\numberline {2.1.2}Subsection 1}{23}{subsection.53}
+\contentsline {subsection}{\numberline {2.1.3}Subsection 2}{23}{subsection.54}
+\contentsline {section}{\numberline {2.2}Main Section 2}{24}{section.55}
+\contentsline {chapter}{\numberline {3}Common Identities In Simplification-Related Functions}{25}{chapter.56}
+\contentsline {section}{\numberline {3.1}Idempotency of $\mathit {simp}$}{25}{section.57}
+\contentsline {subsection}{\numberline {3.1.1}Syntactic Equivalence Under $\mathit {simp}$}{25}{subsection.59}
+\contentsline {subsection}{\numberline {3.1.2}Subsection 2}{25}{subsection.60}
+\contentsline {section}{\numberline {3.2}Main Section 2}{25}{section.61}
+\contentsline {chapter}{\numberline {A}Frequently Asked Questions}{27}{appendix.62}
+\contentsline {section}{\numberline {A.1}How do I change the colors of links?}{27}{section.63}
+\contentsline {chapter}{Bibliography}{29}{appendix*.64}