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A Bialgebraic Review of Deterministic Automata, Regular Expressions and Languages

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Algebra, Meaning, and Computation

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4060))

Abstract

This papers reviews the classical theory of deterministic automata and regular languages from a categorical perspective. The basis is formed by Rutten’s description of the Brzozowski automaton structure in a coalgebraic framework. We enlarge the framework to a so-called bialgebraic one, by including algebras together with suitable distributive laws connecting the algebraic and coalgebraic structure of regular expressions and languages. This culminates in a reformulated proof via finality of Kozen’s completeness result. It yields a complete axiomatisation of observational equivalence (bisimilarity) on regular expressions. We suggest that this situation is paradigmatic for (theoretical) computer science as the study of “generated behaviour”.

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Author information

Authors and Affiliations

  1. Institute for Computing and Information Sciences, Radboud University Nijmegen, P.O. Box 9010, 6500 GL, Nijmegen, The Netherlands

    Bart Jacobs

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  1. Bart Jacobs
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Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology (JAIST),  

    Kokichi Futatsugi

  2. LIX, Projet INRIA TypiCal, École Polytechnique and CNRS, 91400, Palaiseau, France

    Jean-Pierre Jouannaud

  3. CS Dept., University of Illinois at Urbana-Champaign, USA

    José Meseguer

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Jacobs, B. (2006). A Bialgebraic Review of Deterministic Automata, Regular Expressions and Languages. In: Futatsugi, K., Jouannaud, JP., Meseguer, J. (eds) Algebra, Meaning, and Computation. Lecture Notes in Computer Science, vol 4060. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780274_20

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  • DOI: https://doi.org/10.1007/11780274_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35462-8

  • Online ISBN: 978-3-540-35464-2

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