The complexity of definability by open first-order formulas

Autores
Areces, Carlos Eduardo; Campercholi, Miguel Alejandro Carlos; Penazzi, Daniel Eduardo; Ventura, Pablo Gabriel
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this article, we formally define and investigate the computational complexity of the definability problem for open first-order formulas (i.e. quantifier free first-order formulas) with equality. Given a logic L, the L-definability problem for finite structures takes as an input a finite structure A and a target relation T over the domain of A and determines whether there is a formula of L whose interpretation in A coincides with T. We show that the complexity of this problem for open first-order formulas (open definability, for short) is coNP-complete. We also investigate the parametric complexity of the problem and prove that if the size and the arity of the target relation T are taken as parameters, then open definability is coW[1]-complete for every vocabulary τ with at least one, at least binary, relation.
Fil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Campercholi, Miguel Alejandro Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Penazzi, Daniel Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Ventura, Pablo Gabriel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Materia
Definability
Open formulas
First order logic
Complexity
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/145168
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The complexity of definability by open first-order formulasAreces, Carlos EduardoCampercholi, Miguel Alejandro CarlosPenazzi, Daniel EduardoVentura, Pablo GabrielDefinabilityOpen formulasFirst order logicComplexityhttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1In this article, we formally define and investigate the computational complexity of the definability problem for open first-order formulas (i.e. quantifier free first-order formulas) with equality. Given a logic L, the L-definability problem for finite structures takes as an input a finite structure A and a target relation T over the domain of A and determines whether there is a formula of L whose interpretation in A coincides with T. We show that the complexity of this problem for open first-order formulas (open definability, for short) is coNP-complete. We also investigate the parametric complexity of the problem and prove that if the size and the arity of the target relation T are taken as parameters, then open definability is coW[1]-complete for every vocabulary τ with at least one, at least binary, relation.Fil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Campercholi, Miguel Alejandro Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Penazzi, Daniel Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Ventura, Pablo Gabriel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaOxford University Press2020-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/145168Areces, Carlos Eduardo; Campercholi, Miguel Alejandro Carlos; Penazzi, Daniel Eduardo; Ventura, Pablo Gabriel; The complexity of definability by open first-order formulas; Oxford University Press; Logic Journal of the IGPL (print); 28; 6; 12-2020; 1093-11051367-07511368-9894CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/jigpal/article-abstract/28/6/1093/5848645?redirectedFrom=fulltextinfo:eu-repo/semantics/altIdentifier/doi/10.1093/jigpal/jzaa008info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1904.04637info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:02:18Zoai:ri.conicet.gov.ar:11336/145168instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:02:18.425CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The complexity of definability by open first-order formulas
title The complexity of definability by open first-order formulas
spellingShingle The complexity of definability by open first-order formulas
Areces, Carlos Eduardo
Definability
Open formulas
First order logic
Complexity
title_short The complexity of definability by open first-order formulas
title_full The complexity of definability by open first-order formulas
title_fullStr The complexity of definability by open first-order formulas
title_full_unstemmed The complexity of definability by open first-order formulas
title_sort The complexity of definability by open first-order formulas
dc.creator.none.fl_str_mv Areces, Carlos Eduardo
Campercholi, Miguel Alejandro Carlos
Penazzi, Daniel Eduardo
Ventura, Pablo Gabriel
author Areces, Carlos Eduardo
author_facet Areces, Carlos Eduardo
Campercholi, Miguel Alejandro Carlos
Penazzi, Daniel Eduardo
Ventura, Pablo Gabriel
author_role author
author2 Campercholi, Miguel Alejandro Carlos
Penazzi, Daniel Eduardo
Ventura, Pablo Gabriel
author2_role author
author
author
dc.subject.none.fl_str_mv Definability
Open formulas
First order logic
Complexity
topic Definability
Open formulas
First order logic
Complexity
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this article, we formally define and investigate the computational complexity of the definability problem for open first-order formulas (i.e. quantifier free first-order formulas) with equality. Given a logic L, the L-definability problem for finite structures takes as an input a finite structure A and a target relation T over the domain of A and determines whether there is a formula of L whose interpretation in A coincides with T. We show that the complexity of this problem for open first-order formulas (open definability, for short) is coNP-complete. We also investigate the parametric complexity of the problem and prove that if the size and the arity of the target relation T are taken as parameters, then open definability is coW[1]-complete for every vocabulary τ with at least one, at least binary, relation.
Fil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Campercholi, Miguel Alejandro Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Penazzi, Daniel Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Fil: Ventura, Pablo Gabriel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
description In this article, we formally define and investigate the computational complexity of the definability problem for open first-order formulas (i.e. quantifier free first-order formulas) with equality. Given a logic L, the L-definability problem for finite structures takes as an input a finite structure A and a target relation T over the domain of A and determines whether there is a formula of L whose interpretation in A coincides with T. We show that the complexity of this problem for open first-order formulas (open definability, for short) is coNP-complete. We also investigate the parametric complexity of the problem and prove that if the size and the arity of the target relation T are taken as parameters, then open definability is coW[1]-complete for every vocabulary τ with at least one, at least binary, relation.
publishDate 2020
dc.date.none.fl_str_mv 2020-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/145168
Areces, Carlos Eduardo; Campercholi, Miguel Alejandro Carlos; Penazzi, Daniel Eduardo; Ventura, Pablo Gabriel; The complexity of definability by open first-order formulas; Oxford University Press; Logic Journal of the IGPL (print); 28; 6; 12-2020; 1093-1105
1367-0751
1368-9894
CONICET Digital
CONICET
url http://hdl.handle.net/11336/145168
identifier_str_mv Areces, Carlos Eduardo; Campercholi, Miguel Alejandro Carlos; Penazzi, Daniel Eduardo; Ventura, Pablo Gabriel; The complexity of definability by open first-order formulas; Oxford University Press; Logic Journal of the IGPL (print); 28; 6; 12-2020; 1093-1105
1367-0751
1368-9894
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/jigpal/article-abstract/28/6/1093/5848645?redirectedFrom=fulltext
info:eu-repo/semantics/altIdentifier/doi/10.1093/jigpal/jzaa008
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1904.04637
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Oxford University Press
publisher.none.fl_str_mv Oxford University Press
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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