On Tackling the Limits of Resolution in SAT Solving

The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the resolution proof system, for which many hard examples exist. This paper proposes a new problem transformation, which enables reducing the decision problem for formulas in conjunctive normal form (CNF) to the problem of solving maximum satisfiability over Horn formulas. Given the new transformation, the paper proves a polynomial bound on the number of MaxSAT resolution steps for pigeonhole formulas. This result is in clear contrast with earlier results on the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper also establishes the same polynomial bound in the case of modern core-guided MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard for CDCL SAT solvers, show that these can be efficiently solved with modern MaxSAT solvers

Improving Local Search for Structured SAT Formulas via Unit Propagation Based Construct and Cut Initialization (Short Paper)

This work is dedicated to improving local search solvers for the Boolean satisfiability (SAT) problem on structured instances. We propose a construct-and-cut (CnC) algorithm based on unit propagation, which is used to produce initial assignments for local search. We integrate our CnC initialization procedure within several state-of-the-art local search SAT solvers, and obtain the improved solvers. Experiments are carried out with a benchmark encoded from a spectrum repacking project as well as benchmarks encoded from two important mathematical problems namely Boolean Pythagorean Triple and Schur Number Five. The experiments show that the CnC initialization improves the local search solvers, leading to better performance than state-of-the-art SAT solvers based on Conflict Driven Clause Learning (CDCL) solvers

Experimenting a Conflict-Driven Clause Learning Algorithm

International audienceExperimentation of new algorithms is the usual companion section of papers dealing with SAT. However, the behavior of those algorithms is so unpredictable that even strong experiments (hundreds of benchmarks, dozen of solvers) can be still misleading. We present here a set of experiments of very small changes of a canonical Conflict Driven Clause Learning (CDCL) solver and show that even very close versions can lead to very different behaviors. In some cases, the best of them could perfectly have been used to convince the reader of the efficiency of a new method for SAT. This observation can be explained by the lack of real experimental studies of CDCL solvers