# HG changeset patch # User Chengsong # Date 1583326859 0 # Node ID 676440e0a233449ecb54b21b13a194a44a0886c6 # Parent a7c063981fa5304d49db8b88e28e8d8c009228cf daily little report diff -r a7c063981fa5 -r 676440e0a233 twtsevms/twtsevms.tex --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/twtsevms/twtsevms.tex Wed Mar 04 13:00:59 2020 +0000 @@ -0,0 +1,110 @@ +\documentclass[a4paper,UKenglish]{lipics} +\usepackage{graphic} +\usepackage{data} +\usepackage{tikz-cd} +\usepackage{tikz} + +%\usetikzlibrary{graphs} +%\usetikzlibrary{graphdrawing} +%\usegdlibrary{trees} + +%\usepackage{algorithm} +\usepackage{amsmath} +\usepackage{xcolor} +\usepackage[noend]{algpseudocode} +\usepackage{enumitem} +\usepackage{nccmath} +\usepackage{soul} + +\definecolor{darkblue}{rgb}{0,0,0.6} +\hypersetup{colorlinks=true,allcolors=darkblue} +\newcommand{\comment}[1]% +{{\color{red}$\Rightarrow$}\marginpar{\raggedright\small{\bf\color{red}#1}}} + +% \documentclass{article} +%\usepackage[utf8]{inputenc} +%\usepackage[english]{babel} +%\usepackage{listings} +% \usepackage{amsthm} +%\usepackage{hyperref} +% \usepackage[margin=0.5in]{geometry} +%\usepackage{pmboxdraw} + +\title{POSIX Regular Expression Matching and Lexing} +\author{Chengsong Tan} +\affil{King's College London\\ +London, UK\\ +\texttt{chengsong.tan@kcl.ac.uk}} +\authorrunning{Chengsong Tan} +\Copyright{Chengsong Tan} + +\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% +\newcommand{\ZERO}{\mbox{\bf 0}} +\newcommand{\ONE}{\mbox{\bf 1}} +\def\erase{\textit{erase}} +\def\bders{\textit{bders}} +\def\lexer{\mathit{lexer}} +\def\blexer{\textit{blexer}} +\def\fuse{\textit{fuse}} +\def\flatten{\textit{flatten}} +\def\map{\textit{map}} +\def\blexers{\mathit{blexer\_simp}} +\def\simp{\mathit{simp}} +\def\mkeps{\mathit{mkeps}} +\def\bmkeps{\textit{bmkeps}} +\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\flex{\textit{flex}} +\def\rup{r^\uparrow} +\def\retrieve{\textit{retrieve}} +\def\AALTS{\textit{AALTS}} +\def\AONE{\textit{AONE}} +%\theoremstyle{theorem} +%\newtheorem{theorem}{Theorem} +%\theoremstyle{lemma} +%\newtheorem{lemma}{Lemma} +%\newcommand{\lemmaautorefname}{Lemma} +%\theoremstyle{definition} +%\newtheorem{definition}{Definition} +\algnewcommand\algorithmicswitch{\textbf{switch}} +\algnewcommand\algorithmiccase{\textbf{case}} +\algnewcommand\algorithmicassert{\texttt{assert}} +\algnewcommand\Assert[1]{\State \algorithmicassert(#1)}% +% New "environments" +\algdef{SE}[SWITCH]{Switch}{EndSwitch}[1]{\algorithmicswitch\ #1\ \algorithmicdo}{\algorithmicend\ \algorithmicswitch}% +\algdef{SE}[CASE]{Case}{EndCase}[1]{\algorithmiccase\ #1}{\algorithmicend\ \algorithmiccase}% +\algtext*{EndSwitch}% +\algtext*{EndCase}% + + +\begin{document} + +\maketitle + +Hello. +Let us play with the function $f$ on annotated regular expressions: +\begin{center} +$f(\ZERO) = \ZERO$ +$f(_{bs}\ONE) = \textit{bs}$\\ +$f(_{bs}a) = \textit{bs} $\\ +$f(_{bs}r_1\cdot r_2) = \textit{bs} \cdot $ +$f(_{bs}\sum{rs}) = \textit{bs} \cdot \sum\limits_{r \in rs}{f(\textit{r})}$\\ +$f(_{bs}r*) = \textit{bs} \cdot((0 \cdot f(r))\cdot 1) $ +\end{center} + + +\bibliographystyle{plain} +\bibliography{root} + + +\end{document} +