{"title":"An algebraic theory of nondeterministic finite automata","authors":"Roberto Gorrieri","doi":"10.1016/j.jlamp.2025.101055","DOIUrl":null,"url":null,"abstract":"<div><div>A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA <em>N</em>, there exists a process algebraic term <em>p</em> such that its semantics is an NFA isomorphic to <em>N</em>. Moreover, we provide a concise axiomatization of language equivalence: two NFAs <span><math><msub><mrow><mi>N</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> recognize the same language if and only if the associated terms <span><math><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, respectively, can be equated by means of a set of axioms, comprising 7 axioms plus 3 conditional axioms, only.</div></div>","PeriodicalId":48797,"journal":{"name":"Journal of Logical and Algebraic Methods in Programming","volume":"145 ","pages":"Article 101055"},"PeriodicalIF":0.7000,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Logical and Algebraic Methods in Programming","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2352220825000215","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
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Abstract
A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA N, there exists a process algebraic term p such that its semantics is an NFA isomorphic to N. Moreover, we provide a concise axiomatization of language equivalence: two NFAs and recognize the same language if and only if the associated terms and , respectively, can be equated by means of a set of axioms, comprising 7 axioms plus 3 conditional axioms, only.
期刊介绍：
The Journal of Logical and Algebraic Methods in Programming is an international journal whose aim is to publish high quality, original research papers, survey and review articles, tutorial expositions, and historical studies in the areas of logical and algebraic methods and techniques for guaranteeing correctness and performability of programs and in general of computing systems. All aspects will be covered, especially theory and foundations, implementation issues, and applications involving novel ideas.
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