Hierarchies of polynomially solvable satisfiability problems |
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Authors: | Daniele Pretolani |
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Affiliation: | (1) Dipartimento di Informatica, Università di Pisa, Corso Italia 40, I-56125 Pisa, Italy |
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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 {
i
}, where l corresponds to the Generalized Horn class. We propose a family of polynomial hierarchies, where a polynomial hierarchy {
i
} is a sequence of polynomially solvable classes that cover the whole set of CNF formulas, and such that
i
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 l. We discuss and compare the basic properties of the proposed classes; polynomial time algorithms for recognition and solution are provided. |
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Keywords: | |
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