On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | , , , |
Tipo de documento: | Livro |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://hdl.handle.net/10216/90771 |
Resumo: | Extended regular expressions (with complement and intersection) are used in many applications due to their succinctness. In particular, regular expressions extended with intersection only (also called semi-extended) can already be exponentially smaller than standard regular expressions or equivalent nondeterministic finite automata (NFA). For practical purposes it is important to study the average behaviour of conversions between these models. In this paper, we focus on the conversion of regular expressions with intersection to nondeterministic finite automata, using partial derivatives and the notion of support. First, we give a tight upper bound of 2O(n) for the worst-case number of states of the resulting partial derivative automaton, where n is the size of the expression. Using the framework of analytic combinatorics, we then establish an upper bound of (1.056 + o(1))n for its asymptotic average-state complexity, which is significantly smaller than the one for the worst case. (c) IFIP International Federation for Information Processing 2016. |
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On the State Complexity of Partial Derivative Automata For Regular Expressions with IntersectionCiência de computadores, Ciências da computação e da informaçãoComputer science, Computer and information sciencesExtended regular expressions (with complement and intersection) are used in many applications due to their succinctness. In particular, regular expressions extended with intersection only (also called semi-extended) can already be exponentially smaller than standard regular expressions or equivalent nondeterministic finite automata (NFA). For practical purposes it is important to study the average behaviour of conversions between these models. In this paper, we focus on the conversion of regular expressions with intersection to nondeterministic finite automata, using partial derivatives and the notion of support. First, we give a tight upper bound of 2O(n) for the worst-case number of states of the resulting partial derivative automaton, where n is the size of the expression. Using the framework of analytic combinatorics, we then establish an upper bound of (1.056 + o(1))n for its asymptotic average-state complexity, which is significantly smaller than the one for the worst case. (c) IFIP International Federation for Information Processing 2016.20162016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/bookapplication/pdfhttps://hdl.handle.net/10216/90771eng10.1007/978-3-319-41114-9_4Bastos, RBroda, SAntónio MachiaveloNelma MoreiraRogério Reisinfo: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:RCAAP2023-11-29T15:08:45Zoai:repositorio-aberto.up.pt:10216/90771Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:16:40.981457Repositório 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 |
On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection |
title |
On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection |
spellingShingle |
On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection Bastos, R Ciência de computadores, Ciências da computação e da informação Computer science, Computer and information sciences |
title_short |
On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection |
title_full |
On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection |
title_fullStr |
On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection |
title_full_unstemmed |
On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection |
title_sort |
On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection |
author |
Bastos, R |
author_facet |
Bastos, R Broda, S António Machiavelo Nelma Moreira Rogério Reis |
author_role |
author |
author2 |
Broda, S António Machiavelo Nelma Moreira Rogério Reis |
author2_role |
author author author author |
dc.contributor.author.fl_str_mv |
Bastos, R Broda, S António Machiavelo Nelma Moreira Rogério Reis |
dc.subject.por.fl_str_mv |
Ciência de computadores, Ciências da computação e da informação Computer science, Computer and information sciences |
topic |
Ciência de computadores, Ciências da computação e da informação Computer science, Computer and information sciences |
description |
Extended regular expressions (with complement and intersection) are used in many applications due to their succinctness. In particular, regular expressions extended with intersection only (also called semi-extended) can already be exponentially smaller than standard regular expressions or equivalent nondeterministic finite automata (NFA). For practical purposes it is important to study the average behaviour of conversions between these models. In this paper, we focus on the conversion of regular expressions with intersection to nondeterministic finite automata, using partial derivatives and the notion of support. First, we give a tight upper bound of 2O(n) for the worst-case number of states of the resulting partial derivative automaton, where n is the size of the expression. Using the framework of analytic combinatorics, we then establish an upper bound of (1.056 + o(1))n for its asymptotic average-state complexity, which is significantly smaller than the one for the worst case. (c) IFIP International Federation for Information Processing 2016. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016 2016-01-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/book |
format |
book |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://hdl.handle.net/10216/90771 |
url |
https://hdl.handle.net/10216/90771 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1007/978-3-319-41114-9_4 |
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) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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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1799136086746726400 |