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Automated Analysis of Regular Algebra

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Automated Reasoning (IJCAR 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7364))

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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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References

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Author information

Authors and Affiliations

  1. Department of Computer Science, The University of Sheffield, UK

    Simon Foster & Georg Struth

Authors
  1. Simon Foster
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  2. Georg Struth
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Editor information

Editors and Affiliations

  1. Fakultät für Informatik, Technische Universität Wien, Favoritenstr. 9, E185/2, 1040, Wien, Austria

    Bernhard Gramlich

  2. École Polytechnique, INRIA Saclay and Laboratoire d’Informatique, Route de Saclay, 91128, Palaiseau Cedex, France

    Dale Miller

  3. School of Computer Science, University of Manchester, Oxford Road, M13 9PL, Manchester, UK

    Uli Sattler

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© 2012 Springer-Verlag Berlin Heidelberg

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Foster, S., Struth, G. (2012). Automated Analysis of Regular Algebra. In: Gramlich, B., Miller, D., Sattler, U. (eds) Automated Reasoning. IJCAR 2012. Lecture Notes in Computer Science(), vol 7364. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31365-3_22

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  • DOI: https://doi.org/10.1007/978-3-642-31365-3_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31364-6

  • Online ISBN: 978-3-642-31365-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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