# HG changeset patch # User Christian Urban # Date 1350017148 -3600 # Node ID 92b3e287d87e27e066cf83177090c9141c961e12 # Parent d085fe0c086f44d11c2ff485f3571379d7c4d457 slides 4 diff -r d085fe0c086f -r 92b3e287d87e slides04.pdf Binary file slides04.pdf has changed diff -r d085fe0c086f -r 92b3e287d87e slides04.tex --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/slides04.tex Fri Oct 12 05:45:48 2012 +0100 @@ -0,0 +1,381 @@ +\documentclass[dvipsnames,14pt,t]{beamer} +\usepackage{beamerthemeplainculight} +\usepackage[T1]{fontenc} +\usepackage[latin1]{inputenc} +\usepackage{mathpartir} +\usepackage[absolute,overlay]{textpos} +\usepackage{ifthen} +\usepackage{tikz} +\usepackage{pgf} +\usepackage{calc} +\usepackage{ulem} +\usepackage{courier} +\usepackage{listings} +\renewcommand{\uline}[1]{#1} +\usetikzlibrary{arrows} +\usetikzlibrary{automata} +\usetikzlibrary{shapes} +\usetikzlibrary{shadows} +\usetikzlibrary{positioning} +\usetikzlibrary{calc} +\usepackage{graphicx} + +\definecolor{javared}{rgb}{0.6,0,0} % for strings +\definecolor{javagreen}{rgb}{0.25,0.5,0.35} % comments +\definecolor{javapurple}{rgb}{0.5,0,0.35} % keywords +\definecolor{javadocblue}{rgb}{0.25,0.35,0.75} % javadoc + +\lstset{language=Java, + basicstyle=\ttfamily, + keywordstyle=\color{javapurple}\bfseries, + stringstyle=\color{javagreen}, + commentstyle=\color{javagreen}, + morecomment=[s][\color{javadocblue}]{/**}{*/}, + numbers=left, + numberstyle=\tiny\color{black}, + stepnumber=1, + numbersep=10pt, + tabsize=2, + showspaces=false, + showstringspaces=false} + +\lstdefinelanguage{scala}{ + morekeywords={abstract,case,catch,class,def,% + do,else,extends,false,final,finally,% + for,if,implicit,import,match,mixin,% + new,null,object,override,package,% + private,protected,requires,return,sealed,% + super,this,throw,trait,true,try,% + type,val,var,while,with,yield}, + otherkeywords={=>,<-,<\%,<:,>:,\#,@}, + sensitive=true, + morecomment=[l]{//}, + morecomment=[n]{/*}{*/}, + morestring=[b]", + morestring=[b]', + morestring=[b]""" +} + +\lstset{language=Scala, + basicstyle=\ttfamily, + keywordstyle=\color{javapurple}\bfseries, + stringstyle=\color{javagreen}, + commentstyle=\color{javagreen}, + morecomment=[s][\color{javadocblue}]{/**}{*/}, + numbers=left, + numberstyle=\tiny\color{black}, + stepnumber=1, + numbersep=10pt, + tabsize=2, + showspaces=false, + showstringspaces=false} + +% beamer stuff +\renewcommand{\slidecaption}{AFL 04, King's College London, 17.~October 2012} +\newcommand{\bl}[1]{\textcolor{blue}{#1}} +\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions + +\begin{document} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}<1>[t] +\frametitle{% + \begin{tabular}{@ {}c@ {}} + \\[-3mm] + \LARGE Automata and \\[-2mm] + \LARGE Formal Languages (4)\\[3mm] + \end{tabular}} + + \normalsize + \begin{center} + \begin{tabular}{ll} + Email: & christian.urban at kcl.ac.uk\\ + Of$\!$fice: & S1.27 (1st floor Strand Building)\\ + Slides: & KEATS (also home work is there)\\ + \end{tabular} + \end{center} + + +\end{frame}} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}Last Week\end{tabular}} + +Last week I showed you + +\begin{itemize} +\item tokenizer + +\item tokenization identifies lexeme in an input stream of characters (or string) +and categorizes them into tokens + +\item maximal munch rule +\end{itemize} + +\url{http://www.technologyreview.com/tr10/?year=2011} + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}The Derivative of a Rexp\end{tabular}} + +\begin{center} +\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}} + \bl{der c ($\varnothing$)} & \bl{$\dn$} & \bl{$\varnothing$} & \\ + \bl{der c ($\epsilon$)} & \bl{$\dn$} & \bl{$\varnothing$} & \\ + \bl{der c (d)} & \bl{$\dn$} & \bl{if c $=$ d then $\epsilon$ else $\varnothing$} & \\ + \bl{der c (r$_1$ + r$_2$)} & \bl{$\dn$} & \bl{(der c r$_1$) + (der c r$_2$)} & \\ + \bl{der c (r$_1$ $\cdot$ r$_2$)} & \bl{$\dn$} & \bl{if nullable r$_1$}\\ + & & \bl{then ((der c r$_1$) $\cdot$ r$_2$) + (der c r$_2$)}\\ + & & \bl{else (der c r$_1$) $\cdot$ r$_2$}\\ + \bl{der c (r$^*$)} & \bl{$\dn$} & \bl{(der c r) $\cdot$ (r$^*$)}\\ + \end{tabular} +\end{center} + +``the regular expression after \bl{c} has been recognised'' + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] + +For this we defined the set \bl{Der c A} as + +\begin{center} +\bl{Der c A $\dn$ $\{$ s $|$ c::s $\in$ A$\}$ } +\end{center} + +which is called the semantic derivative of a set +and proved + +\begin{center} +\bl{$L$(der c r) $=$ Der c ($L$(r))} +\end{center} + + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}The Idea of the Algorithm\end{tabular}} + +If we want to recognise the string \bl{abc} with regular expression \bl{r} +then\medskip + +\begin{enumerate} +\item \bl{Der a ($L$(r))}\pause +\item \bl{Der b (Der a ($L$(r)))} +\item \bl{Der c (Der b (Der a ($L$(r))))}\pause +\item finally we test whether the empty string is in set\pause\medskip +\end{enumerate} + +The matching algorithm works similarly, just over regular expression than sets. +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] + +Input: string \bl{abc} and regular expression \bl{r} + +\begin{enumerate} +\item \bl{der a r} +\item \bl{der b (der a r)} +\item \bl{der c (der b (der a r))}\pause +\item finally check whether the latter regular expression can match the empty string +\end{enumerate} + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] + +We need to prove + +\begin{center} +\bl{$L$(der c r) $=$ Der c ($L$(r))} +\end{center} + +by induction on the regular expression. + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}Proofs about Rexp\end{tabular}} + +\begin{itemize} +\item \bl{$P$} holds for \bl{$\varnothing$}, \bl{$\epsilon$} and \bl{c}\bigskip +\item \bl{$P$} holds for \bl{r$_1$ + r$_2$} under the assumption that \bl{$P$} already +holds for \bl{r$_1$} and \bl{r$_2$}.\bigskip +\item \bl{$P$} holds for \bl{r$_1$ $\cdot$ r$_2$} under the assumption that \bl{$P$} already +holds for \bl{r$_1$} and \bl{r$_2$}. +\item \bl{$P$} holds for \bl{r$^*$} under the assumption that \bl{$P$} already +holds for \bl{r}. +\end{itemize} + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}Proofs about Natural Numbers\\ and Strings\end{tabular}} + +\begin{itemize} +\item \bl{$P$} holds for \bl{$0$} and +\item \bl{$P$} holds for \bl{$n + 1$} under the assumption that \bl{$P$} already +holds for \bl{$n$} +\end{itemize}\bigskip + +\begin{itemize} +\item \bl{$P$} holds for \bl{\texttt{""}} and +\item \bl{$P$} holds for \bl{$c\!::\!s$} under the assumption that \bl{$P$} already +holds for \bl{$s$} +\end{itemize} + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[t] +\frametitle{\begin{tabular}{c}Regular Expressions\end{tabular}} + +\begin{center} + \begin{tabular}{@ {}rrl@ {\hspace{13mm}}l} + \bl{r} & \bl{$::=$} & \bl{$\varnothing$} & null\\ + & \bl{$\mid$} & \bl{$\epsilon$} & empty string / "" / []\\ + & \bl{$\mid$} & \bl{c} & character\\ + & \bl{$\mid$} & \bl{r$_1$ $\cdot$ r$_2$} & sequence\\ + & \bl{$\mid$} & \bl{r$_1$ + r$_2$} & alternative / choice\\ + & \bl{$\mid$} & \bl{r$^*$} & star (zero or more)\\ + \end{tabular}\bigskip\pause + \end{center} + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}Languages\end{tabular}} + +A \alert{language} is a set of strings.\bigskip + +A \alert{regular expression} specifies a set of strings or language.\bigskip + +A language is \alert{regular} iff there exists +a regular expression that recognises all its strings.\bigskip\bigskip\pause + +\textcolor{gray}{not all languages are regular, e.g.~\bl{a$^n$b$^n$}.} +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[t] +\frametitle{\begin{tabular}{c}Regular Expressions\end{tabular}} + +\begin{center} + \begin{tabular}{@ {}rrl@ {\hspace{13mm}}l} + \bl{r} & \bl{$::=$} & \bl{$\varnothing$} & null\\ + & \bl{$\mid$} & \bl{$\epsilon$} & empty string / "" / []\\ + & \bl{$\mid$} & \bl{c} & character\\ + & \bl{$\mid$} & \bl{r$_1$ $\cdot$ r$_2$} & sequence\\ + & \bl{$\mid$} & \bl{r$_1$ + r$_2$} & alternative / choice\\ + & \bl{$\mid$} & \bl{r$^*$} & star (zero or more)\\ + \end{tabular}\bigskip + \end{center} + +How about ranges \bl{[a-z]}, \bl{r$^\text{+}$} and \bl{!r}? + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}Negation of Regular Expr's\end{tabular}} + +\begin{itemize} +\item \bl{!r} \hspace{6mm} (everything that \bl{r} cannot recognise)\medskip +\item \bl{$L$(!r) $\dn$ UNIV - $L$(r)}\medskip +\item \bl{nullable (!r) $\dn$ not (nullable(r))}\medskip +\item \bl{der\,c\,(!r) $\dn$ !(der\,c\,r)} +\end{itemize} + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}Regular Exp's for Lexing\end{tabular}} + +Lexing separates strings into ``words'' / components. + +\begin{itemize} +\item Identifiers (non-empty strings of letters or digits, starting with a letter) +\item Numbers (non-empty sequences of digits omitting leading zeros) +\item Keywords (else, if, while, \ldots) +\item White space (a non-empty sequence of blanks, newlines and tabs) +\item Comments +\end{itemize} + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}Automata\end{tabular}} + +A deterministic finite automaton consists of: + +\begin{itemize} +\item a set of states +\item one of these states is the start state +\item some states are accepting states, and +\item there is transition function\medskip + +\small +which takes a state as argument and a character and produces a new state\smallskip\\ +this function might not always be defined +\end{itemize} + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: +