A bialgebraic review of deterministic automata, regular expressions and languages

被引：0
|
作者：
Jacobs, Bart [1 ]
机构：
[1] Radboud Univ Nijmegen, Inst Comp & Informat Sci, NL-6500 GL Nijmegen, Netherlands
来源：
ALGEBRA, MEANING, AND COMPUTATION: ESSAYS DEDICATED TO JOSEPH A. GOGUEN ON THE OCCASION OF HIS 65TH BIRTHDAY | 2006年 / 4060卷
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D O I：
暂无
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
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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收藏
页码：375 / 404
页数：30
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