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(2006) Algebra, meaning, and computation, Dordrecht, Springer.
A bialgebraic review of deterministic automata, regular expressions and languages
Bart Jacobs
pp. 375-404
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".
Publication details
DOI: 10.1007/11780274_20
Full citation:
Jacobs, B. (2006)., A bialgebraic review of deterministic automata, regular expressions and languages, in K. Futatsugi, J. Jouannaud & J. Meseguer (eds.), Algebra, meaning, and computation, Dordrecht, Springer, pp. 375-404.
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