\documentclass{article}

\usepackage{charter}

\usepackage{hyperref}

\usepackage{amssymb}

\usepackage{amsmath}

\usepackage[T1]{fontenc}

\usepackage{listings}

\usepackage{xcolor}

\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}%

\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

\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}

\begin{document}

\section*{Handout 2}

Having specified what problem our matching algorithm, $match$, is supposed to solve, namely

for a given regular expression $r$ and string $s$ answer $true$ if and only if

\[

s \in L(r)

\]

\noindent

Clearly we cannot use the function $L$ directly in order to solve this problem, because in general

the set of strings $L$ returns is infinite (recall what $L(a^*)$ is). In such cases there is no algorithm

then can test exhaustively, whether a string is member of this set.

The algorithm we define below consists of two parts. One is the function $nullable$ which takes a

\end{document}

%%% Local Variables: 

%%% mode: latex

%%% TeX-master: t

%%% End: