Towards provably complete stochastic search algorithms for satisfiability

Abstract

This paper proposes a stochastic, and complete, backtrack search algorithm for Propositional Satisfiability (SAT). In recent years, randomization has become pervasive in SAT algorithms. Incomplete algorithms for SAT, for example the ones based on local search, often resort to randomization. Complete algorithms also resort to randomization. These include, state-of-the-art backtrack search SAT algorithms that often randomize variable selection heuristics. Moreover, it is plain that the introduction of randomization in other components of backtrack search SAT algorithms can potentially yield new competitive search strategies. As a result, we propose a stochastic backtrack search algorithm for SAT, that randomizes both the variable selection and the backtrack steps of the algorithm. In addition, we describe and compare different organizations of stochastic backtrack search. Finally, experimental results provide empirical evidence that the new search algorithm for SAT results in a very competitive approach for solving hard real-world instances. © Springer-Verlag Berlin Heidelberg 2001.