| author | urbanc |
| Tue, 08 Feb 2011 19:54:23 +0000 | |
| changeset 83 | f438f4dbaada |
| parent 82 | 14b12b5de6d3 |
| child 88 | 1436fc451bb9 |
| permissions | -rw-r--r-- |
| 24 | 1 |
\documentclass{llncs}
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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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\usepackage{pdfsetup}
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\usepackage{ot1patch}
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\usepackage{times}
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\usepackage{proof}
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52
4a517c6ac07d
tuning of the syntax; needs the stmaryrd latex package
urbanc
parents:
24
diff
changeset
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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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\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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\begin{document}
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\title{A Formalisation of the Myhill-Nerode Theorem\\ based on Regular
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Expressions (Proof Pearl)} |
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\author{Chunhan Wu\inst{1} \and Xingjuan Zhang\inst{1} \and Christian Urban\inst{2}}
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\institute{PLA University, China \and TU Munich, Germany}
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\maketitle |
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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 |
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only mentioning on the side a connection with regular expressions. |
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Unfortunately, automata are a hassle for formalisations in HOL-based |
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theorem provers. The reason is that they need to be represented as graphs, |
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matrices or functions, none of which are inductive datatypes. Also |
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operations, such as disjoint unions of graphs, are not easily formalisiable |
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in HOL. In contrast, regular expressions can be defined conveniently |
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as datatype and a corresponding reasoning infrastructure comes for |
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free. We show in this paper that a central result from formal |
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language theory---the Myhill-Nerode theorem---can be recreated |
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using only regular expressions. |
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\end{abstract}
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\input{session}
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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: |