48 lines
1.6 KiB
TeX
48 lines
1.6 KiB
TeX
\documentclass[11pt,a4paper]{article}
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\usepackage{isabelle,isabellesym}
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\usepackage{eufrak}
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% this should be the last package used
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\usepackage{pdfsetup}
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% urls in roman style, theory text in math-similar italics
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\urlstyle{rm}
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\isabellestyle{it}
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\begin{document}
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\title{Regular Sets, Expressions, Derivatives and Relation Algebra}
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\author{Alexander Krauss, Tobias Nipkow,\\
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Chunhan Wu, Xingyuan Zhang and Christian Urban}
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\maketitle
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\begin{abstract}
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This is a library of constructions on regular expressions and languages. It
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provides the operations of concatenation, Kleene star and left-quotients of
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languages. A theory of derivatives and partial derivatives is
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provided. Arden's lemma and finiteness of partial derivatives is
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established. A simple regular expression matcher based on Brozowski's
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derivatives is proved to be correct. An executable equivalence checker for
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regular expressions is verified; it does not need automata but works directly
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on regular expressions. By mapping regular expressions to binary relations, an
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automatic and complete proof method for (in)equalities of binary relations
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over union, concatenation and (reflexive) transitive closure is obtained.
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For an exposition of the equivalence checker for regular and relation
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algebraic expressions see the paper by Krauss and Nipkow~\cite{KraussN-JAR}.
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Extended regular expressions with complement and intersection
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are also defined and an equivalence checker is provided.
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\end{abstract}
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\tableofcontents
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% include generated text of all theories
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\input{session}
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\bibliographystyle{abbrv}
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\bibliography{root}
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\end{document}
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