GPU Parallelism for SAT Solving Heuristics

Modern SAT solvers employ a number of smart techniques and strategies to achieve maximum efficiency in solving the Boolean Satisfiability problem. Among all components of a solver, the branching heuristics plays a crucial role in affecting the performance of the entire solver. Traditionally, the main branching heuristics that have appeared in the literature have been classified as look-back heuristics or look-ahead heuristics. As SAT technology has evolved, the former have become more and more preferable, for their demand for less computational effort. Graphics Processor Units (GPUs) are massively parallel devices that have spread enormously over the past few decades and offer great computing power at a relatively low cost. We describe how to exploit such computational power to efficiently implement look-ahead heuristics. Our aim is to “rehabilitate” these heuristics, by showing their effectiveness in the contest of a parallel SAT solver

Hiding Satisfying Assignments: Two are Better than One

The evaluation of incomplete satisfiability solvers depends critically on the availability of hard satisfiable instances. A plausible source of such instances consists of random k-SAT formulas whose clauses are chosen uniformly from among all clauses satisfying some randomly chosen truth assignment A. Unfortunately, instances generated in this manner tend to be relatively easy and can be solved efficiently by practical heuristics. Roughly speaking, as the formula's density increases, for a number of different algorithms, A acts as a stronger and stronger attractor. Motivated by recent results on the geometry of the space of satisfying truth assignments of random k-SAT and NAE-k-SAT formulas, we introduce a simple twist on this basic model, which appears to dramatically increase its hardness. Namely, in addition to forbidding the clauses violated by the hidden assignment A, we also forbid the clauses violated by its complement, so that both A and complement of A are satisfying. It appears that under this "symmetrization'' the effects of the two attractors largely cancel out, making it much harder for algorithms to find any truth assignment. We give theoretical and experimental evidence supporting this assertion.Comment: Preliminary version appeared in AAAI 200

Integrating Conflict Driven Clause Learning to Local Search

This article introduces SatHyS (SAT HYbrid Solver), a novel hybrid approach for propositional satisfiability. It combines local search and conflict driven clause learning (CDCL) scheme. Each time the local search part reaches a local minimum, the CDCL is launched. For SAT problems it behaves like a tabu list, whereas for UNSAT ones, the CDCL part tries to focus on minimum unsatisfiable sub-formula (MUS). Experimental results show good performances on many classes of SAT instances from the last SAT competitions

On the Hardness of SAT with Community Structure

Recent attempts to explain the effectiveness of Boolean satisfiability (SAT) solvers based on conflict-driven clause learning (CDCL) on large industrial benchmarks have focused on the concept of community structure. Specifically, industrial benchmarks have been empirically found to have good community structure, and experiments seem to show a correlation between such structure and the efficiency of CDCL. However, in this paper we establish hardness results suggesting that community structure is not sufficient to explain the success of CDCL in practice. First, we formally characterize a property shared by a wide class of metrics capturing community structure, including "modularity". Next, we show that the SAT instances with good community structure according to any metric with this property are still NP-hard. Finally, we study a class of random instances generated from the "pseudo-industrial" community attachment model of Gir\'aldez-Cru and Levy. We prove that, with high probability, instances from this model that have relatively few communities but are still highly modular require exponentially long resolution proofs and so are hard for CDCL. We also present experimental evidence that our result continues to hold for instances with many more communities. This indicates that actual industrial instances easily solved by CDCL may have some other relevant structure not captured by the community attachment model.Comment: 23 pages. Full version of a SAT 2016 pape

Accelerating SAT solving with best-first-search

Solvers for Boolean satisfiability (SAT), like other algorithms for NP-complete problems, tend to have a heavy-tailed runtime distribution. Successful SAT solvers make use of frequent restarts to mitigate this problem by abandoning unfruitful parts of the search space after some time. Although frequent restarting works fairly well, it is a quite simplistic technique that does not do anything explicitly to make the next try better than the previous one. In this paper, we suggest a more sophisticated method: using a best-first-search approach to quickly move between different parts of the search space. This way, the search can always focus on the most promising region. We investigate empirically how the performance of frequent restarts, best-first-search, and a combination of the two compare to each other. Our findings indicate that the combined method works best, improving 36-43\% on the performance of frequent restarts on the used set of benchmark problems