About: On Minimum Representations of Matched Formulas

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://jair.org/media/4517/live-4517-8363-jair.pdf
Description	A Boolean formula in conjunctive normal form (CNF) is called matched if the system of sets of variables which appear in individual clauses has a system of distinct representatives. Each matched CNF is trivially satisfiable (each clause can be satisfied by its representative variable). Another property which is easy to see, is that the class of matched CNFs is not closed under partial assignment of truth values to variables. This latter property leads to a fact (proved here) that given two matched CNFs it is co-NP complete to decide whether they are logically equivalent. The construction in this proof leads to another result: a much shorter and simpler proof of the fact that the Boolean minimization problem for matched CNFs is a complete problem for the second level of the polynomial hierarchy. The main result of this paper deals with the structure of clause minimum CNFs. We prove here that if a Boolean function f admits a representation by a matched CNF then every clause minimum CNF representation of f is matched. A Boolean formula in conjunctive normal form (CNF) is called matched if the system of sets of variables which appear in individual clauses has a system of distinct representatives. Each matched CNF is trivially satisfiable (each clause can be satisfied by its representative variable). Another property which is easy to see, is that the class of matched CNFs is not closed under partial assignment of truth values to variables. This latter property leads to a fact (proved here) that given two matched CNFs it is co-NP complete to decide whether they are logically equivalent. The construction in this proof leads to another result: a much shorter and simpler proof of the fact that the Boolean minimization problem for matched CNFs is a complete problem for the second level of the polynomial hierarchy. The main result of this paper deals with the structure of clause minimum CNFs. We prove here that if a Boolean function f admits a representation by a matched CNF then every clause minimum CNF representation of f is matched. (en)
Title	On Minimum Representations of Matched Formulas On Minimum Representations of Matched Formulas (en)
skos:prefLabel	On Minimum Representations of Matched Formulas On Minimum Representations of Matched Formulas (en)
skos:notation	RIV/00216208:11320/14:10285651!RIV15-MSM-11320___
http://linked.open...avai/riv/aktivita	I
http://linked.open...avai/riv/aktivity	I
http://linked.open...iv/cisloPeriodika	12/2014
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Kučera, Petr Čepek, Ondřej Gurský, Štefan
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	34324
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/14:10285651
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Matched Formulas; Minimum Representations (en)
http://linked.open.../riv/klicoveSlovo	Matched Formulas Minimum Representations
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[9FDFA44DBC47]
http://linked.open...i/riv/nazevZdroje	Journal of Artificial Intelligence Research
http://linked.open...in/vavai/riv/obor	IN
http://linked.open...ichTvurcuVysledku	3 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	51
http://linked.open...iv/tvurceVysledku	Kučera, Petr Čepek, Ondřej Gurský, Štefan
issn	1076-9757
number of pages	17 (xsd:int)
http://bibframe.org/vocab/doi	10.1613/jair.4517
http://localhost/t...ganizacniJednotka	11320

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