1 \documentclass[a4paper,UKenglish]{lipics}

     2 \usepackage{graphic}

     3 \usepackage{data}

     4 \usepackage{tikz-cd}

     5 \usepackage{tikz}

     6 

     7 %\usetikzlibrary{graphs}

     8 %\usetikzlibrary{graphdrawing}

     9 %\usegdlibrary{trees}

    10 

    11 %\usepackage{algorithm}

    12 \usepackage{amsmath}

    13 \usepackage{xcolor}

    14 \usepackage[noend]{algpseudocode}

    15 \usepackage{enumitem}

    16 \usepackage{nccmath}

    17 \usepackage{soul}

    18 

    19 \definecolor{darkblue}{rgb}{0,0,0.6}

    20 \hypersetup{colorlinks=true,allcolors=darkblue}

    21 \newcommand{\comment}[1]%

    22 {{\color{red}$\Rightarrow$}\marginpar{\raggedright\small{\bf\color{red}#1}}}

    23 

    24 % \documentclass{article}

    25 %\usepackage[utf8]{inputenc}

    26 %\usepackage[english]{babel}

    27 %\usepackage{listings}

    28 % \usepackage{amsthm}

    29 %\usepackage{hyperref}

    30 % \usepackage[margin=0.5in]{geometry}

    31 %\usepackage{pmboxdraw}

    32  

    33 \title{POSIX Regular Expression Matching and Lexing}

    34 \author{Chengsong Tan}

    35 \affil{King's College London\\

    36 London, UK\\

    37 \texttt{chengsong.tan@kcl.ac.uk}}

    38 \authorrunning{Chengsong Tan}

    39 \Copyright{Chengsong Tan}

    40 

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

    42 \newcommand{\ZERO}{\mbox{\bf 0}}

    43 \newcommand{\ONE}{\mbox{\bf 1}}

    44 \def\erase{\textit{erase}}

    45 \def\bders{\textit{bders}}

    46 \def\lexer{\mathit{lexer}}

    47 \def\blexer{\textit{blexer}}

    48 \def\fuse{\textit{fuse}}

    49 \def\flatten{\textit{flatten}}

    50 \def\map{\textit{map}}

    51 \def\blexers{\mathit{blexer\_simp}}

    52 \def\simp{\mathit{simp}}

    53 \def\mkeps{\mathit{mkeps}}

    54 \def\bmkeps{\textit{bmkeps}}

    55 \def\inj{\mathit{inj}}

    56 \def\Empty{\mathit{Empty}}

    57 \def\Left{\mathit{Left}}

    58 \def\Right{\mathit{Right}}

    59 \def\Stars{\mathit{Stars}}

    60 \def\Char{\mathit{Char}}

    61 \def\Seq{\mathit{Seq}}

    62 \def\Der{\mathit{Der}}

    63 \def\nullable{\mathit{nullable}}

    64 \def\Z{\mathit{Z}}

    65 \def\S{\mathit{S}}

    66 \def\flex{\textit{flex}}

    67 \def\rup{r^\uparrow}

    68 \def\retrieve{\textit{retrieve}}

    69 \def\AALTS{\textit{AALTS}}

    70 \def\AONE{\textit{AONE}}

    71 %\theoremstyle{theorem}

    72 %\newtheorem{theorem}{Theorem}

    73 %\theoremstyle{lemma}

    74 %\newtheorem{lemma}{Lemma}

    75 %\newcommand{\lemmaautorefname}{Lemma}

    76 %\theoremstyle{definition}

    77 %\newtheorem{definition}{Definition}

    78 \algnewcommand\algorithmicswitch{\textbf{switch}}

    79 \algnewcommand\algorithmiccase{\textbf{case}}

    80 \algnewcommand\algorithmicassert{\texttt{assert}}

    81 \algnewcommand\Assert[1]{\State \algorithmicassert(#1)}%

    82 % New "environments"

    83 \algdef{SE}[SWITCH]{Switch}{EndSwitch}[1]{\algorithmicswitch\ #1\ \algorithmicdo}{\algorithmicend\ \algorithmicswitch}%

    84 \algdef{SE}[CASE]{Case}{EndCase}[1]{\algorithmiccase\ #1}{\algorithmicend\ \algorithmiccase}%

    85 \algtext*{EndSwitch}%

    86 \algtext*{EndCase}%

    87 

    88 

    89 \begin{document}

    90 

    91 \maketitle

    92 

    93 Hello.

    94 Let us play with the function $f$ on annotated regular expressions:

    95 \begin{center}

    96 $f(\ZERO) = \ZERO$

    97 $f(_{bs}\ONE) = \textit{bs}$\\

    98 $f(_{bs}a) = \textit{bs} $\\

    99 $f(_{bs}r_1\cdot r_2) = \textit{bs} \cdot $

   100 $f(_{bs}\sum{rs}) = \textit{bs} \cdot \sum\limits_{r \in rs}{f(\textit{r})}$\\

   101 $f(_{bs}r*) = \textit{bs} \cdot((0 \cdot f(r))\cdot 1) $

   102 \end{center}

   103 

   104 

   105 \bibliographystyle{plain}

   106 \bibliography{root}

   107 

   108 

   109 \end{document}

   110