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A Bialgebraic Review of Regular Expressions, Deterministic Automata and Languages

B. Jacobs, A Bialgebraic Review of Regular Expressions, Deterministic Automata and Languages, Technical Report ICIS-R05003, Institute for Computing and Information Sciences, Radboud University of Nijmegen.

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".

Bart Jacobs. Bialgebras. Enough said.

By Ehud Lamm at 2005-09-08 13:14 | Category Theory | login or register to post comments | other blogs | 9631 reads

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By Ehud Lamm at 2005-09-08 15:10 | LtU Forum | login or register to post comments | other blogs | 5399 reads