Automated Analysis of Regular Algebra

  • Simon Foster
  • Georg Struth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7364)

Abstract

Regular algebras axiomatise the equational theory of regular expressions. We use Isabelle/HOL’s automated theorem provers and counterexample generators to study the regular algebras of Boffa, Conway, Kozen and Salomaa, formalise their soundness and completeness (relative to a deep result by Krob) and engineer their hierarchy. Proofs range from fully automatic axiomatic and inductive calculations to integrated higher-order reasoning with numbers, sets and monoid submorphisms. In combination with Isabelle’s simplifiers and structuring mechanisms, automated deduction provides powerful support to the working mathematician beyond first-order reasoning.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Simon Foster
    • 1
  • Georg Struth
    • 1
  1. 1.Department of Computer ScienceThe University of SheffieldUK

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