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Proof Pearl: Regular Expression Equivalence and Relation Algebra

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Abstract

We describe and verify an elegant equivalence checker for regular expressions. It works by constructing a bisimulation relation between (derivatives of) regular expressions. By mapping regular expressions to binary relations, an automatic and complete proof method for (in)equalities of binary relations over union, composition and (reflexive) transitive closure is obtained. The verification is carried out in the theorem prover Isabelle/HOL, yielding a practically useful decision procedure.

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  1. Institut für Informatik, Technische Universität München, Munich, Germany

    Alexander Krauss & Tobias Nipkow

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  1. Alexander Krauss
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  2. Tobias Nipkow
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Correspondence to Alexander Krauss.

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Krauss, A., Nipkow, T. Proof Pearl: Regular Expression Equivalence and Relation Algebra. J Autom Reasoning 49, 95–106 (2012). https://doi.org/10.1007/s10817-011-9223-4

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  • DOI: https://doi.org/10.1007/s10817-011-9223-4

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