| author | urbanc |
| Fri, 26 Aug 2011 17:29:07 +0000 | |
| changeset 219 | 296930182fe1 |
| parent 200 | 204856ef5573 |
| child 233 | e2dc11e12e0b |
| permissions | -rw-r--r-- |
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\documentclass{ita}
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\usepackage{isabelle}
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\usepackage{isabellesym}
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\usepackage{amsmath}
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\usepackage{amssymb}
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\usepackage{tikz}
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\usepackage{pgf}
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\usetikzlibrary{arrows,automata,decorations,fit,calc}
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\usetikzlibrary{shapes,shapes.arrows,snakes,positioning}
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\usepgflibrary{shapes.misc} % LATEX and plain TEX and pure pgf
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\usetikzlibrary{matrix}
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\usepackage{pdfsetup}
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\usepackage{ot1patch}
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\usepackage{times}
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%%\usepackage{proof}
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%%\usepackage{mathabx}
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tuning of the syntax; needs the stmaryrd latex package
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\usepackage{stmaryrd}
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\urlstyle{rm}
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\isabellestyle{it}
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\renewcommand{\isastyleminor}{\it}%
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\renewcommand{\isastyle}{\normalsize\it}%
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\newcommand*{\threesim}{%
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\mathrel{\vcenter{\offinterlineskip
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\hbox{$\sim$}\vskip-.35ex\hbox{$\sim$}\vskip-.35ex\hbox{$\sim$}}}}
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\def\dn{\,\stackrel{\mbox{\scriptsize def}}{=}\,}
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\renewcommand{\isasymequiv}{$\dn$}
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\renewcommand{\isasymemptyset}{$\varnothing$}
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\renewcommand{\isacharunderscore}{\mbox{$\_\!\_$}}
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\newcommand{\isasymcalL}{\ensuremath{\cal{L}}}
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\newcommand{\isasymbigplus}{\ensuremath{\bigplus}}
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\newcommand{\bigplus}{\mbox{\Large\bf$+$}}
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\begin{document}
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\title{A Formalisation of the Myhill-Nerode Theorem\\ based on Regular
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Expressions} |
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\thanks{This is a revised and expanded version of \cite{WuZhangUrban11}.}
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\author{Chunhan Wu}\address{PLA University of Science and Technology, China}
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\author{Xingyuan Zhang}\sameaddress{1}
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\author{Christian Urban}\address{TU Munich,
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added an example for non-regularity and continuation lemma (the example does not yet work)
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Germany}\secondaddress{corresponding author}
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\subjclass{68Q45}
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\keywords{Myhill-Nerode theorem, regular expressions, Isabelle theorem prover}
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\begin{abstract}
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There are numerous textbooks on regular languages. Nearly all of them |
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introduce the subject by describing finite automata and only mentioning on the |
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side a connection with regular expressions. Unfortunately, automata are difficult |
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to formalise in HOL-based theorem provers. The reason is that |
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they need to be represented as graphs, matrices or functions, none of which |
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are inductive datatypes. Also convenient operations for disjoint unions of |
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graphs, matrices and functions are not easily formalisiable in HOL. In contrast, regular |
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expressions can be defined conveniently as a datatype and a corresponding |
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reasoning infrastructure comes for free. We show in this paper that a central |
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result from formal language theory---the Myhill-Nerode theorem---can be |
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recreated using only regular expressions. |
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\end{abstract}
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\maketitle |
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\input{session}
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%%\mbox{}\\[-10mm]
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\bibliographystyle{plain}
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\bibliography{root}
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\end{document}
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%%% Local Variables: |
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%%% mode: latex |
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%%% TeX-master: t |
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%%% End: |