Local Autarkies Searching for the Dynamic Partition of CNF Formulae

In this paper an original dynamic partition of formulae in conjunctive normal form (CNF) is presented. It is based on the autarky concept first introduced by Monien and Speckenmeyer and further investigated by Kullmann and Van Gelder. Intuitively, an autarky is a partial assignment satisfying some clauses while not affecting any literal in any other clause, leading to a partition of the CNF formula. Autarkies can play a dramatic role in the efficiency of modern SAT solvers. The approach in this paper aims to dynamically extend the current partial assignment to a local autarky thanks to an inference rule based on unit propagation. More precisely, at each node of the search tree, it is checked whether the current decision literal can be made monotone by subsuming all the clauses where it appears negatively. The formal framework is detailed and its technical features discussed.