Automating resolution is NP-Hard

We show that the problem of finding a Resolution refutation that is at most polynomially longer than a shortest one is NP-hard. In the parlance of proof complexity, Resolution is not automatable unless P = NP. Indeed, we show that it is NP-hard to distinguish between formulas that have Resolution re...

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Detalles Bibliográficos
Autores: Atserias, Albert|||0000-0002-3732-1989, Muller, Moritz Martin
Tipo de recurso: artículo
Fecha de publicación:2020
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:2117/337031
Acceso en línea:https://hdl.handle.net/2117/337031
https://dx.doi.org/10.1145/3409472
Access Level:acceso abierto
Palabra clave:Computational complexity
Resolution
Proof search
NP-hardness
Complexitat computacional
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
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spelling Automating resolution is NP-HardAtserias, Albert|||0000-0002-3732-1989Muller, Moritz MartinComputational complexityResolutionProof searchNP-hardnessComplexitat computacionalÀrees temàtiques de la UPC::Informàtica::Informàtica teòricaWe show that the problem of finding a Resolution refutation that is at most polynomially longer than a shortest one is NP-hard. In the parlance of proof complexity, Resolution is not automatable unless P = NP. Indeed, we show that it is NP-hard to distinguish between formulas that have Resolution refutations of polynomial length and those that do not have subexponential length refutations. This also implies that Resolution is not automatable in subexponential time or quasi-polynomial time unless NP is included in SUBEXP or QP, respectively.Both authors were partially funded by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant agreement ERC-2014-CoG 648276 (AUTAR). First author partially funded by MICCIN grant TIN2016-76573-C2-1P (TASSAT3).Peer Reviewed20202020-09-0120212021-02-08journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/337031https://dx.doi.org/10.1145/3409472reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengEuropean Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 648276 A Unified Theory of Algorithmic Relaxationsopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3370312026-05-27T15:37:01Z
dc.title.none.fl_str_mv Automating resolution is NP-Hard
title Automating resolution is NP-Hard
spellingShingle Automating resolution is NP-Hard
Atserias, Albert|||0000-0002-3732-1989
Computational complexity
Resolution
Proof search
NP-hardness
Complexitat computacional
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
title_short Automating resolution is NP-Hard
title_full Automating resolution is NP-Hard
title_fullStr Automating resolution is NP-Hard
title_full_unstemmed Automating resolution is NP-Hard
title_sort Automating resolution is NP-Hard
dc.creator.none.fl_str_mv Atserias, Albert|||0000-0002-3732-1989
Muller, Moritz Martin
author Atserias, Albert|||0000-0002-3732-1989
author_facet Atserias, Albert|||0000-0002-3732-1989
Muller, Moritz Martin
author_role author
author2 Muller, Moritz Martin
author2_role author
dc.subject.none.fl_str_mv Computational complexity
Resolution
Proof search
NP-hardness
Complexitat computacional
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
topic Computational complexity
Resolution
Proof search
NP-hardness
Complexitat computacional
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
description We show that the problem of finding a Resolution refutation that is at most polynomially longer than a shortest one is NP-hard. In the parlance of proof complexity, Resolution is not automatable unless P = NP. Indeed, we show that it is NP-hard to distinguish between formulas that have Resolution refutations of polynomial length and those that do not have subexponential length refutations. This also implies that Resolution is not automatable in subexponential time or quasi-polynomial time unless NP is included in SUBEXP or QP, respectively.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-09-01
2021
2021-02-08
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/2117/337031
https://dx.doi.org/10.1145/3409472
url https://hdl.handle.net/2117/337031
https://dx.doi.org/10.1145/3409472
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 648276 A Unified Theory of Algorithmic Relaxations
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.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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