Approximate formulae for a logic that capture classes of computational complexity

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Logic Journal of IGPL following peer review. The definitive publisher-authenticated version Arratia, Argimiro; Ortiz, Carlos E. Approximate formulae for a logic that capture classes of computational complexity....

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Detalles Bibliográficos
Autores: Arratia Quesada, Argimiro Alejandro|||0000-0003-1551-420X, Ortiz, Carlos E.
Tipo de recurso: artículo
Fecha de publicación:2009
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/8034
Acceso en línea:https://hdl.handle.net/2117/8034
https://dx.doi.org/10.1093/jigpal/jzn031
Access Level:acceso abierto
Palabra clave:Computer logic
Computational complexity
Complexitat computacional
Lògica informàtica
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica::Aplicacions informàtiques a la física i l‘enginyeria
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spelling Approximate formulae for a logic that capture classes of computational complexityArratia Quesada, Argimiro Alejandro|||0000-0003-1551-420XOrtiz, Carlos E.Computer logicComputational complexityComplexitat computacionalLògica informàticaÀrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitatÀrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica::Aplicacions informàtiques a la física i l‘enginyeriaThis is a pre-copy-editing, author-produced PDF of an article accepted for publication in Logic Journal of IGPL following peer review. The definitive publisher-authenticated version Arratia, Argimiro; Ortiz, Carlos E. Approximate formulae for a logic that capture classes of computational complexity. Logic Journal of IGPL, 2009, vol. 17, p. 131-154 is available online at: http://jigpal.oxfordjournals.org/cgi/reprint/17/1/131?maxtoshow=&hits=10&RESULTFORMAT=&fulltext=Approximate+formulae+for+a+logic+that+capture+classes+of+computational+complexity&searchid=1&FIRSTINDEX=0&resourcetype=HWCITThis paper presents a syntax of approximate formulae suited for the logic with counting quantifiers SOLP. This logic was formalised by us in [1] where, among other properties, we showed the following facts: (i) In the presence of a built–in (linear) order, SOLP can describe NP–complete problems and some of its fragments capture the classes P and NL; (ii) weakening the ordering relation to an almost order we can separate meaningful fragments, using a combinatorial tool adapted to these languages. The purpose of our approximate formulae is to provide a syntactic approximation to the logic SOLP, enhanced with a built-in order, that should be complementary of the semantic approximation based on almost orders, by means of producing logics where problems are syntactically described within a small counting error. We introduce a concept of strong expressibility based on approximate formulae, and show that for many fragments of SOLP with built-in order, including ones that capture P and NL, expressibility and strong expressibility are equivalent. We state and prove a Bridge Theorem that links expressibility in fragments of SOLP over almost-ordered structures to strong expressibility with respect to approximate formulae for the corresponding fragments over ordered structures. A consequence of these results is that proving inexpressibility over fragments of SOLP with built-in order could be done by proving inexpressibility over the corresponding fragments with built-in almost order, where separation proofs are allegedly easier.Peer ReviewedOxford University Press20092009-02-0120102010-07-07journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/8034https://dx.doi.org/10.1093/jigpal/jzn031reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/80342026-05-27T15:37:01Z
dc.title.none.fl_str_mv Approximate formulae for a logic that capture classes of computational complexity
title Approximate formulae for a logic that capture classes of computational complexity
spellingShingle Approximate formulae for a logic that capture classes of computational complexity
Arratia Quesada, Argimiro Alejandro|||0000-0003-1551-420X
Computer logic
Computational complexity
Complexitat computacional
Lògica informàtica
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica::Aplicacions informàtiques a la física i l‘enginyeria
title_short Approximate formulae for a logic that capture classes of computational complexity
title_full Approximate formulae for a logic that capture classes of computational complexity
title_fullStr Approximate formulae for a logic that capture classes of computational complexity
title_full_unstemmed Approximate formulae for a logic that capture classes of computational complexity
title_sort Approximate formulae for a logic that capture classes of computational complexity
dc.creator.none.fl_str_mv Arratia Quesada, Argimiro Alejandro|||0000-0003-1551-420X
Ortiz, Carlos E.
author Arratia Quesada, Argimiro Alejandro|||0000-0003-1551-420X
author_facet Arratia Quesada, Argimiro Alejandro|||0000-0003-1551-420X
Ortiz, Carlos E.
author_role author
author2 Ortiz, Carlos E.
author2_role author
dc.subject.none.fl_str_mv Computer logic
Computational complexity
Complexitat computacional
Lògica informàtica
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica::Aplicacions informàtiques a la física i l‘enginyeria
topic Computer logic
Computational complexity
Complexitat computacional
Lògica informàtica
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica::Aplicacions informàtiques a la física i l‘enginyeria
description This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Logic Journal of IGPL following peer review. The definitive publisher-authenticated version Arratia, Argimiro; Ortiz, Carlos E. Approximate formulae for a logic that capture classes of computational complexity. Logic Journal of IGPL, 2009, vol. 17, p. 131-154 is available online at: http://jigpal.oxfordjournals.org/cgi/reprint/17/1/131?maxtoshow=&hits=10&RESULTFORMAT=&fulltext=Approximate+formulae+for+a+logic+that+capture+classes+of+computational+complexity&searchid=1&FIRSTINDEX=0&resourcetype=HWCIT
publishDate 2009
dc.date.none.fl_str_mv 2009
2009-02-01
2010
2010-07-07
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/8034
https://dx.doi.org/10.1093/jigpal/jzn031
url https://hdl.handle.net/2117/8034
https://dx.doi.org/10.1093/jigpal/jzn031
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 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:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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