Sufficient and necessary conditions for solution finding in valuation-based systems

Valuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notion of solution. Typical examples are satisfying assignments in constraint systems, models in logics or solutions to li...

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Detalles Bibliográficos
Autores: Roca Lacostena, Jordi|||0000-0003-1651-9504, Cerquides, Jesús, Pouly, Marc
Tipo de recurso: artículo
Fecha de publicación:2019
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:2117/168518
Acceso en línea:https://hdl.handle.net/2117/168518
https://dx.doi.org/10.1016/j.ijar.2019.08.006
Access Level:acceso abierto
Palabra clave:Algebra
Àlgebra
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
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spelling Sufficient and necessary conditions for solution finding in valuation-based systemsRoca Lacostena, Jordi|||0000-0003-1651-9504Cerquides, JesúsPouly, MarcAlgebraÀlgebraÀrees temàtiques de la UPC::Matemàtiques i estadística::ÀlgebraValuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notion of solution. Typical examples are satisfying assignments in constraint systems, models in logics or solutions to linear equation systems. Many widely used dynamic programming algorithms for optimization problems rely on low treewidth decompositions and can be understood as particular cases of a single algorithmic scheme for finding solutions in a valuation algebra. The most encompassing description of this algorithmic scheme to date has been proposed by Pouly and Kohlas together with sufficient conditions for its correctness. Unfortunately, the formalization relies on a theorem for which we provide counterexamples. In spite of that, the mainline of Pouly and Kohlas’ theory is correct, although some of the necessary conditions have to be revised. In this paper we analyze the impact that the counter-examples have on the theory, and rebuild the theory providing correct sufficient conditions for the algorithms. Furthermore, we also provide necessary conditions for the algorithms, allowing for a sharper characterization of when the algorithmic scheme can be applied.Peer Reviewed20192019-11-0120192019-09-20journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/168518https://dx.doi.org/10.1016/j.ijar.2019.08.006reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1685182026-05-27T15:37:01Z
dc.title.none.fl_str_mv Sufficient and necessary conditions for solution finding in valuation-based systems
title Sufficient and necessary conditions for solution finding in valuation-based systems
spellingShingle Sufficient and necessary conditions for solution finding in valuation-based systems
Roca Lacostena, Jordi|||0000-0003-1651-9504
Algebra
Àlgebra
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
title_short Sufficient and necessary conditions for solution finding in valuation-based systems
title_full Sufficient and necessary conditions for solution finding in valuation-based systems
title_fullStr Sufficient and necessary conditions for solution finding in valuation-based systems
title_full_unstemmed Sufficient and necessary conditions for solution finding in valuation-based systems
title_sort Sufficient and necessary conditions for solution finding in valuation-based systems
dc.creator.none.fl_str_mv Roca Lacostena, Jordi|||0000-0003-1651-9504
Cerquides, Jesús
Pouly, Marc
author Roca Lacostena, Jordi|||0000-0003-1651-9504
author_facet Roca Lacostena, Jordi|||0000-0003-1651-9504
Cerquides, Jesús
Pouly, Marc
author_role author
author2 Cerquides, Jesús
Pouly, Marc
author2_role author
author
dc.subject.none.fl_str_mv Algebra
Àlgebra
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
topic Algebra
Àlgebra
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
description Valuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notion of solution. Typical examples are satisfying assignments in constraint systems, models in logics or solutions to linear equation systems. Many widely used dynamic programming algorithms for optimization problems rely on low treewidth decompositions and can be understood as particular cases of a single algorithmic scheme for finding solutions in a valuation algebra. The most encompassing description of this algorithmic scheme to date has been proposed by Pouly and Kohlas together with sufficient conditions for its correctness. Unfortunately, the formalization relies on a theorem for which we provide counterexamples. In spite of that, the mainline of Pouly and Kohlas’ theory is correct, although some of the necessary conditions have to be revised. In this paper we analyze the impact that the counter-examples have on the theory, and rebuild the theory providing correct sufficient conditions for the algorithms. Furthermore, we also provide necessary conditions for the algorithms, allowing for a sharper characterization of when the algorithmic scheme can be applied.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-11-01
2019
2019-09-20
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/2117/168518
https://dx.doi.org/10.1016/j.ijar.2019.08.006
url https://hdl.handle.net/2117/168518
https://dx.doi.org/10.1016/j.ijar.2019.08.006
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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
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