Local Search for Unsatisfiability

Abstract

Abstract. Local search is widely applied to satisfiable SAT problems, and on some classes outperforms backtrack search. An intriguing challenge posed by Selman, Kautz and McAllester in 1997 is to use it instead to prove unsatisfiability. We investigate two distinct approaches. Firstly we apply standard local search to a reformulation of the problem, such that a solution to the reformulation corresponds to a refutation of the original problem. Secondly we design a greedy randomised resolution algorithm that will eventually discover proofs of any size while using bounded memory. We show experimentally that both approaches can refute some problems more quickly than backtrack search.

An overview of parallel SAT solving

“…Given a CNF formula, complete SAT solvers can either find a solution or prove that no solution exists. In contrast, incomplete SAT solvers can prove either satisfiability [89] or unsatisfiability [80]. Hence, incomplete solvers have applications in problems for which is known beforehand that only satisfiability or unsatisfiability is required to be proven.…”

Local Search Based on Conflict Analysis for the Satisfiability Problem

“…In [11], a greedy algorithm based on the extended resolution is proposed but limited to treat unsatisfiable instances with few variables. In [12], the authors propose two approaches based on local search to prove inconsistency. The first one is based on the reformulation of the input instance and the second is a greedy search for randomized resolution.…”

Encoding First Order Proofs in SAT

“…[16] has explored the idea of encoding a propositional resolution proof itself in propositional logic. Our emphasis is different from that paper.…”

“…In order to do this, we need to decide what kind of proof should be encoded. One possibility would be to encode a resolution proof, as has been done in [16], although in that paper propositional proofs were encoded and not first order proofs. We chose instead to encode a connection tableau proof.…”