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Hierarchies of polynomially solvable satisfiability problems

Hierarchies of polynomially solvable satisfiability problems In this paper, we introduce general techniques for extending classes of polynomially solvable SAT instances. We generalize the approach of Gallo and Scutellà, who defined the hierarchy {Γ i }, where Γl corresponds to the Generalized Horn class. We propose a family of polynomial hierarchies, where a polynomial hierarchy {Π i } is a sequence of polynomially solvable classes that cover the whole set of CNF formulas, and such that Π i ∩ Π i+1 fori≥0. Following a different approach, based on a new decomposition technique, we define the class of Split-Horn formulas, which is an extension of Γl. We discuss and compare the basic properties of the proposed classes; polynomial time algorithms for recognition and solution are provided. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

Hierarchies of polynomially solvable satisfiability problems

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References (16)

Publisher
Springer Journals
Copyright
Copyright
Subject
Computer Science; Artificial Intelligence; Mathematics, general; Computer Science, general; Complex Systems
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/BF02127974
Publisher site
See Article on Publisher Site

Abstract

In this paper, we introduce general techniques for extending classes of polynomially solvable SAT instances. We generalize the approach of Gallo and Scutellà, who defined the hierarchy {Γ i }, where Γl corresponds to the Generalized Horn class. We propose a family of polynomial hierarchies, where a polynomial hierarchy {Π i } is a sequence of polynomially solvable classes that cover the whole set of CNF formulas, and such that Π i ∩ Π i+1 fori≥0. Following a different approach, based on a new decomposition technique, we define the class of Split-Horn formulas, which is an extension of Γl. We discuss and compare the basic properties of the proposed classes; polynomial time algorithms for recognition and solution are provided.

Journal

Annals of Mathematics and Artificial IntelligenceSpringer Journals

Published: Aug 13, 2005

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