We present Regular-SAT, an extension of Boolean Satisfiability based on a class of many-valued CNF formulas. Regular-SAT shares many properties with Boolean SAT, which allows us to generalize some of the best known SAT results and apply them to Regular-SAT. In addition, Regular-SAT has a number of advantages over Boolean SAT. Most importantly, it produces more compact encodings that capture pro...

We establish the satisfiability threshold for random $k$-SAT all $k\ge k_0$, with $k_0$ an absolute constant. That is, there exists a limiting density $\alpha_{\rm sat}(k)$ such that formula of clause $\alpha$ is high probability satisfiable $\alpha\lt \alpha_{\rm sat}$, and unsatisfiable $\alpha>\alpha_{\rm sat}$. show given explicitly by one-step replica symmetry breaking prediction from stat...

An interesting strategy called configuration checking (CC) was recently proposed to handle the cycling problem in local search for Minimum Vertex Cover. A natural question is whether this CC also works SAT. The direct application of did not result stochastic (SLS) algorithms that can compete with current best SLS In paper, we propose a new heuristic based on SAT, which aspiration (CCA). It used...

This paper presents a reduction from the problem of solving parity games to the satisfiability problem in propositional logic (SAT). The reduction is done in two stages, first into difference logic, i.e. SAT combined with the theory of integer differences, an instance of the SAT modulo theories (SMT) framework. In the second stage the integer variables and constraints of the difference logic en...

In this paper, we describe and evaluate three different techniques for translating pseudoboolean constraints (linear constraints over boolean variables) into clauses that can be handled by a standard SAT-solver. We show that by applying a proper mix of translation techniques, a SAT-solver can perform on a par with the best existing native pseudo-boolean solvers. This is particularly valuable in...

We introduce the submodular Max-SAT problem. This problem is a natural generalization of the classical Max-SAT problem in which the additive objective function is replaced by a submodular one. We develop a randomized linear-time 2/3-approximation algorithm for the problem. Our algorithm is applicable even for the online variant of the problem. We also establish hardness results for both the onl...

Recently, edge matching puzzles, an NP-complete problem, have received, thanks to money-prized contests, considerable attention from wide audiences. We consider these competitions not only a challenge for SAT/CSP solving techniques but also as an opportunity to showcase the advances in the SAT/CSP community to a general audience. This paper studies the NP-complete problem of edge matching puzzl...

Theorem proving is a challenging task for formal verification of systems. There exist many efforts to efficiently solve this problem, based for example on rewriting rules and/or SAT-based techniques. We propose an alternative of SAT-based techniques by using instead a counting SAT-based technique (denoted also #SAT). A SAT solver tests if a propositional formula F has at least one truth assignm...

We study how propositional satissability (SAT) problems can be reformulated as constraint satisfaction problems (CSPs). We analyse four diierent mappings of SAT problems into CSPs. For each mapping , we compare theoretically the performance of systematic algorithms like FC and MAC applied to the encoding against the Davis-Putnam procedure applied to the original SAT problem. We also compare loc...