Generating all maximal models of a Boolean expression
We examine the computational problem of generating all maximal models of a Boolean expression in CNF. We give a resolution-like method that reduces the unnegated variables of an expression while preserving its set of maximal models. We present an output-polynomial algorithm for the 2CNF case and we...
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| Vydáno v: | Information processing letters Ročník 74; číslo 3; s. 157 - 162 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Amsterdam
Elsevier B.V
31.05.2000
Elsevier Sequoia S.A |
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| ISSN: | 0020-0190, 1872-6119 |
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| Abstract | We examine the computational problem of generating all maximal models of a Boolean expression in CNF. We give a resolution-like method that reduces the unnegated variables of an expression while preserving its set of maximal models. We present an output-polynomial algorithm for the 2CNF case and we show that the problem cannot be solved in output-polynomial time in the case of Horn expressions, unless
P=
NP
, despite an affinity of this case to the recently subexponentially solved transversal hypergraph problem. The problem is of course trivial for 1-valid and anti-Horn expressions, and open for exclusive-ors; it is NP-hard in all other cases. |
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| AbstractList | We examine the computational problem of generating all maximal models of a Boolean expression in CNF. We give a resolution-like method that reduces the unnegated variables of an expression while preserving its set of maximal models. We present an output-polynomial algorithm for the 2CNF case and we show that the problem cannot be solved in output-polynomial time in the case of Horn expressions, unless
P=
NP
, despite an affinity of this case to the recently subexponentially solved transversal hypergraph problem. The problem is of course trivial for 1-valid and anti-Horn expressions, and open for exclusive-ors; it is NP-hard in all other cases. The computational problem of generating all maximal models of a Boolean expression in CNF is examined. A resolution-like method that reduces the unnegated variables of an expression while preserving its set of maximal models is given. An output-polynomial algorithm for the 2CNF case is presented and it is shown that the problem cannot be solved in output polynomial time in the case of Horn expressions, unless p=NP, despite an affinity of this case to the recently subexponentially solved transversal hypergraph problem. The problem is of course trivial for 1-valid and anti-Horn expressions, and open for exclusive-ors; it is NP-hard in all other cases. We examine the computational problem of generating all maximal models of a Boolean expression in CNF. We give a resolution-like method that reduces the unnegated variables of an expression while preserving its set of maximal models. We present an output-polynomial algorithm for the 2CNF case and we show that the problem cannot be solved in output-polynomial time in the case of Horn expressions, unless P identical with NP, despite an affinity of this case to the recently subexponentially solved transversal hypergraph problem. The problem is of course trivial for 1-valid and anti-Horn expressions, and open for exclusive-ors; it is NP-hard in all other cases. |
| Author | Kavvadias, Dimitris J. Sideri, Martha Stavropoulos, Elias C. |
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| Cites_doi | 10.1016/0004-3702(90)90010-W 10.1006/jagm.1996.0062 10.1145/4221.4223 10.1016/0004-3702(89)90067-2 10.1016/0004-3702(92)90027-U 10.1016/0020-0190(92)90049-2 10.1016/0020-0190(88)90065-8 10.1137/S0097539795285114 10.1006/inco.1995.1087 10.1137/S0097539793250299 10.1007/BF02136172 10.1016/S0304-3975(96)00202-2 |
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| Keywords | Output-polynomial Transversal hypergraph Algorithms Computational complexity Maximal model generation |
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| SubjectTerms | Algorithms Boolean Computational complexity Computer programming Graphs Maximal model generation Output-polynomial Studies Transversal hypergraph |
| Title | Generating all maximal models of a Boolean expression |
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