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\documentclass[runningheads]{llncs}
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\usepackage{isabelle}
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\usepackage{isabellesym}
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%%\usepackage{proof}
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%%\usepackage{mathabx}
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\usepackage{stmaryrd}
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\titlerunning{Proving the Priority Inheritance Protocol Correct}
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262
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\urlstyle{rm}
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\def\dn{\,\stackrel{\mbox{\scriptsize def}}{=}\,}
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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 (Proof Pearl)}
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\author{Chunhan Wu\inst{1} \and Xingyuan Zhang\inst{1} \and Christian Urban\inst{2}}
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\institute{PLA University of Science and Technology, China \and TU Munich, Germany}
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\maketitle
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%\mbox{}\\[-10mm]
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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 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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\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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