Deciding Kleene algebra terms equivalence in Coq

Detalhes bibliográficos
Autor(a) principal: Nelma Moreira
Data de Publicação: 2015
Outros Autores: David Pereira, Simao Melo de Sousa
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://repositorio-aberto.up.pt/handle/10216/90768
Resumo: This paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based on automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.
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spelling Deciding Kleene algebra terms equivalence in CoqCiências da computação e da informaçãoComputer and information sciencesThis paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based on automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://repositorio-aberto.up.pt/handle/10216/90768eng2352-220810.1016/j.jlamp.2014.12.004Nelma MoreiraDavid PereiraSimao Melo de Sousainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-29T14:44:44Zoai:repositorio-aberto.up.pt:10216/90768Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:07:40.678498Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Deciding Kleene algebra terms equivalence in Coq
title Deciding Kleene algebra terms equivalence in Coq
spellingShingle Deciding Kleene algebra terms equivalence in Coq
Nelma Moreira
Ciências da computação e da informação
Computer and information sciences
title_short Deciding Kleene algebra terms equivalence in Coq
title_full Deciding Kleene algebra terms equivalence in Coq
title_fullStr Deciding Kleene algebra terms equivalence in Coq
title_full_unstemmed Deciding Kleene algebra terms equivalence in Coq
title_sort Deciding Kleene algebra terms equivalence in Coq
author Nelma Moreira
author_facet Nelma Moreira
David Pereira
Simao Melo de Sousa
author_role author
author2 David Pereira
Simao Melo de Sousa
author2_role author
author
dc.contributor.author.fl_str_mv Nelma Moreira
David Pereira
Simao Melo de Sousa
dc.subject.por.fl_str_mv Ciências da computação e da informação
Computer and information sciences
topic Ciências da computação e da informação
Computer and information sciences
description This paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based on automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://repositorio-aberto.up.pt/handle/10216/90768
url https://repositorio-aberto.up.pt/handle/10216/90768
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2352-2208
10.1016/j.jlamp.2014.12.004
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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