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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{proof}
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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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\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{King's College London, United Kingdom}\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. From this theorem many closure
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properties of regular languages follow.
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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:
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