A distribution method for solving SAT in grids

Abstract. The emerging large-scale computational grid infrastructure is providing an interesting platform for massive distributed computations. In this paper the problem of exploiting such computational grids for solving challenging propositional satisfiability problem (SAT) instances is studied. When designing a distributed algorithm for a large loosely coupled computational grid, a number of grid specific problems need to be tackled including the heterogeneity of the resources, inherent communication delays, and high failure probabilities of grid jobs. In this work a novel distribution method for solving SAT problem instances, called scattering, is introduced. The key advantages of scattering are that it can be used in conjunction with any sequential SAT solver (including industrial black box solvers), the distribution heuristic is strictly separated from the heuristic used in sequential solving, and it requires no communication between processes solving subproblems but still allows coordination of such processes. An implementation of the method has been developed for NorduGrid, a large widely distributed production-level grid running in Scandinavia. The implementation has been benchmarked with test cases including random 3SAT and challenging industrial benchmarks used in previous SAT competitions.

Efficient and formal generalized symbolic execution

Programs that manipulate dynamic heap objects are difficult to analyze due to issues like aliasing. Lazy initialization algorithm enables the classical symbolic execution to handle such programs. Despite its successes, there are two unresolved issues: (1) inefficiency; (2) lack of formal study. For the inefficiency issue, we have proposed two improved algorithms that give significant analysis time reduction over the original lazy initialization algorithm. In this article, we formalize the lazy initialization algorithm and the improved algorithms as operational semantics of a core subset of the Java Virtual Machine (JVM) instructions, and prove that all algorithms are relatively sound and complete with respect to the JVM concrete semantics. Finally, we conduct a set of extensive experiments that compare the three algorithms and demonstrate the efficiency of the improved algorithms

Frying the Egg, Roasting the Chicken: Unit Deletions in DRAT Proofs

The final publication is available via https://doi.org/ 10.1145/3372885.3373821.The clausal proof format DRAT is the standard de facto to certify SAT solvers' unsatisfiability results. DRAT proofs act as logs of clause inferences and clause deletions in the solver. The non-monotonic nature of the proof system makes deletions relevant. State-of-the-art proof checkers ignore deletions of unit clauses, differing from the standard in meaningful ways that require adaptions when proofs are generated or used for purposes other than checking. On the other hand, dealing with unit deletions in the proof checker breaks many of the usual invariants used for efficiency reasons. Furthermore, many SAT solvers introduce spurious unit deletions in proofs. These deletions are never intended to be applied in the checker but are nevertheless introduced, making many proofs generated by state-of-the-art solvers incorrect. We present the first competitive DRAT checker that honors unit deletions, as well as fixes for the spurious deletion issue in proof generation. Our experimental results confirm that unit deletions can be applied with similar average performance to state-of-the-art checkers. We also confirm that a large fraction of the proofs generated during the last SAT solving competition do not respect the DRAT standard. This result was confirmed with proof incorrectness certificates that were independently validated. We find that our proof incorrectness certificates can be of help when debugging SAT solvers and DRAT checkers.Fonds zur Förderung der Wissenschaftlichen ForschungWiener Wissenschafts-, Forschungs- und Technologiefonds (WWTF