Backdoors to q-Horn

Abstract

The class $$\text {q-Horn}$$q-Horn, introduced by Boros, Crama and Hammer in 1990, is one of the largest known classes of propositional CNF formulas for which satisfiability can be decided in polynomial time. This class properly contains the fundamental classes of Horn and 2-CNF formulas as well as the class of renamable (or disguised) Horn formulas. In this paper we extend this class so that its favorable algorithmic properties can be made accessible to formulas that are outside but "close" to this class. We show that deciding satisfiability is fixed-parameter tractable parameterized by the distance of the given formula from $$\text {q-Horn}$$q-Horn. The distance is measured by the smallest number of variables that we need to delete from the formula in order to get a $$\text {q-Horn}$$q-Horn formula, i.e., the size of a smallest deletion backdoor set into the class $$\text {q-Horn}$$q-Horn. This result generalizes known fixed-parameter tractability results for satisfiability decision with respect to the parameters distance from Horn, 2-CNF, and renamable Horn.