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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.
Annals of Mathematics and Artificial Intelligence – Springer Journals
Published: Aug 13, 2005
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