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\documentclass{llncs}
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\def\dn{\,\stackrel{\mbox{\scriptsize def}}{=}\,}
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\renewcommand{\isacharunderscore}{\mbox{$\_\!\_$}}
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\begin{document}
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\title{A Formalisation of the Myhill-Nerode Theorem\\ based on Regular Expressions}
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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 they need to be represented as graphs
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or matrices, neither of which can be easily defined as datatype. Also
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operations, such as disjoint union of graphs, are not easily formalisiable
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in HOL. In contrast, regular expressions can be defined easily
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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:
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