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, obtaining a family of polynomial hierarchies, where one such polynomial hierarchy is a sequence of nested polynomially solvable classes that cover the whole set of CNF formulas. Following a different approach, based on a new decomposition technique, we define the class of Split-Horn formulas, which is a proper extension of the Generalized Horn formulas defined by Yamasaki e Doshita. We discuss and compare the basic properties of the proposed classes; polynomial time recognition and solution algorithms are provided.