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

Diversification and Intensification in Parallel {SAT} Solving

International audienceIn this paper, we explore the two well-known principles of diversification and intensification in portfolio-based parallel SAT solving. These dual concepts play an important role in several search algorithms including local search, and appear to be a key point in modern parallel SAT solvers. To study their trade-off, we define two roles for the computational units. Some of them classified as Masters perform an original search strategy, ensuring diversification. The remaining units, classified as Slaves are there to intensify their master's strategy. Several important questions have to be answered. The first one is what information should be given to a slave in order to intensify a given search effort? The second one is, how often, a subordinated unit has to receive such information? Finally, the question of finding the number of subordinated units along their connections with the search efforts has to be answered. Our results lead to an original intensification strategy which outperforms the best parallel SAT solver, and solves some open SAT instances

Deterministic Parallel (DP)2LL

Microsoft Research Cambridge, MSR-TR-2011-47Parallel Satisfiability is now recognized as an important research area. The wide deployment of multicore platforms combined with the availability of open and challenging SAT instances are behind this recognition. However, the current parallel SAT solvers suffer from a non-deterministic behavior. This is the consequence of their architectures which rely on weak synchronizing in an attempt to maximize performance. This behavior is a clear downside for practitioners, who are used to both runtime and solution reproducibility. In this paper, we propose the first Deterministic Parallel DPLL engine. It is based on a stateof- the-art parallel portfolio architecture and relies on a controlled synchronizing of the different threads. Our experimental results clearly show that our approach preserves the performance of the parallel portfolio approach while ensuring full reproducibility of the results

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

CadiBack: Extracting Backbones with CaDiCaL

The backbone of a satisfiable formula is the set of literals that are true in all its satisfying assignments. Backbone computation can improve a wide range of SAT-based applications, such as verification, fault localization and product configuration. In this tool paper, we introduce a new backbone extraction tool called CadiBack. It takes advantage of unique features available in our state-of-the-art SAT solver CaDiCaL including transparent inprocessing and single clause assumptions, which have not been evaluated in this context before. In addition, CaDiCaL is enhanced with an improved algorithm to support model rotation by utilizing watched literal data structures. In our comprehensive experiments with a large number of benchmarks, CadiBack solves 60% more instances than the state-of-the-art backbone extraction tool MiniBones. Our tool is thoroughly tested with fuzzing, internal correctness checking and cross-checking on a large benchmark set. It is publicly available as open source, well documented and easy to extend

A logical deduction based clause learning algorithm for Boolean satisfiability problems

Clause learning is the key component of modern SAT solvers, while conflict analysis based on the implication graph is the mainstream technology to generate the learnt clauses. Whenever a clause in the clause database is falsified by the current variable assignments, the SAT solver will try to analyze the reason by using different cuts (i.e., the Unique Implication Points) on the implication graph. Those schemes reflect only the conflict on the current search subspace, does not reflect the inherent conflict directly involved in the rest space. In this paper, we propose a new advanced clause learning algorithm based on the conflict analysis and the logical deduction, which reconstructs a linear logical deduction by analyzing the relationship of different decision variables between the backjumping level and the current decision level. The logical deduction result is then added into the clause database as a newly learnt clause. The resulting implementation in Minisat improves the state-of-the-art performance in SAT solving

An Iterative Path-Breaking Approach with Mutation and Restart Strategies for the MAX-SAT Problem

Although Path-Relinking is an effective local search method for many combinatorial optimization problems, its application is not straightforward in solving the MAX-SAT, an optimization variant of the satisfiability problem (SAT) that has many real-world applications and has gained more and more attention in academy and industry. Indeed, it was not used in any recent competitive MAX-SAT algorithms in our knowledge. In this paper, we propose a new local search algorithm called IPBMR for the MAX-SAT, that remedies the drawbacks of the Path-Relinking method by using a careful combination of three components: a new strategy named Path-Breaking to avoid unpromising regions of the search space when generating trajectories between two elite solutions; a weak and a strong mutation strategies, together with restarts, to diversify the search; and stochastic path generating steps to avoid premature local optimum solutions. We then present experimental results to show that IPBMR outperforms two of the best state-of-the-art MAX-SAT solvers, and an empirical investigation to identify and explain the effect of the three components in IPBMR