A Bialgebraic Review of Deterministic Automata, Regular Expressions and Languages

  • Bart Jacobs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4060)


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”.


Regular Expression Natural Transformation Operational Semantic Follow Diagram Commute Commutative Monoid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bart Jacobs
    • 1
  1. 1.Institute for Computing and Information SciencesRadboud University NijmegenNijmegenThe Netherlands

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