The recently developed massively parallel satisfiability (SAT) solver HordeSAT was designed in a modular way to allow the integration of any sequential CDCL-based SAT solver in its core. We integrated the QCDCL-based quantified Boolean formula (QBF) solver DepQBF in HordeSAT to obtain a massively parallel QBF solver—HordeQBF. In this paper we describe the details of this integration and report on results of the experimental evaluation of HordeQBF’s performance. HordeQBF achieves superlinear average and median speedup on the hard application instances of the 2014 QBF Gallery.
Approaches to parallel QBF solving are based on shared and distributed memory architectures. PQSolve @cite_1 is an early parallel DPLL @cite_6 solver without knowledge sharing. It comes with a dynamic master slave framework implemented using the message passing interface (MPI) @cite_25 . Search space is partitioned among master and slaves by variable assignments. QMiraXT @cite_22 is a multithreaded QCDCL solver with search space partitioning. PAQuBE @cite_13 is an MPI-based parallel variant of the QCDCL solver QuBE @cite_10 . Clause and cube sharing in PAQuBE can be adapted dynamically at run time. Search space is partitioned like in the SAT solver PSATO based on @cite_16 . The MPI-based solver MPI -DepQBF @cite_18 implements a master worker architecture without knowledge sharing. A worker consists of an instance of the QCDCL solver DepQBF @cite_23 . The master balances the workload by generating subproblems defined by variable assignments (assumptions), which are solved by the workers. Parallel solving approaches have also been presented for quantified CSPs @cite_20 and non-PCNF QBFs @cite_14 .
@cite_18 @cite_14 @cite_22 @cite_10 @cite_1 @cite_6 @cite_23 @cite_16 @cite_13 @cite_25 @cite_20
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In this paper we present the parallel QBF Solver PaQuBE. This new solver leverages the additional computational power that can be exploited from modern computer architectures, from pervasive multi-core boxes to clusters and grids, to solve more relevant instances faster than previous generation solvers. Furthermore, PaQuBE's progressive MPI based parallel framework is the first to support advanced knowledge sharing in which solution cubes as well as conflict clauses can be exchanged between solvers. Knowledge sharing plays a critical role in the performance of PaQuBE. However, due to the overhead associated with sending and receiving MPI messages, and the restricted communication network bandwidth available between solvers, it is essential to optimize not only what information is shared, but the way in which it is shared. In this context, we compare multiple conflict clause and solution cube sharing strategies, and finally show that an adaptive method provides the best overall results. Inspired by recent work on parallel SAT solving, we present a lightweight approach for solving quantified Boolean formulas (QBFs) in parallel. In particular, our approach uses a sequential state-of-the-art QBF solver to evaluate subformulas in working processes. It abstains from globally exchanging information between the workers, but keeps learnt information only locally. To this end, we equipped the state-of-the-art QBF solver DepQBF with assumption-based reasoning and integrated it in our novel solver MPIDepQBF as backend solver. Extensive experiments on standard computers as well as on the supercomputer Tsubame show the impact of our approach. This work presents a novel strategy for improving SAT solver performance by using concurrency. Rather than aiming to parallelize search, we use concurrency to aid a conventional CDCL search procedure. More concretely, our work extends a conventional CDCL SAT solver with a second computation thread, which is solely used to strengthen the clauses learned by the solver. This provides a simple and natural way to exploit the availability of multi-core hardware. We have employed our technique to extend two well established solvers, MiniSAT and Glucose. Despite its conceptual simplicity the technique yields a significant improvement of those solvers' performances, in particular for unsatisfiable benchmarks. For such benchmarks an extensive empirical evaluation revealed a remarkably consistent reduction of the wall clock time required to determine unsatisfiability, as well as an ability to solve more benchmarks in the same CPU time. The proposed technique can be applied in combination with existing parallel SAT solving techniques, including both portfolio and search space splitting approaches. The approach presented here can thus be seen as orthogonal to those existing techniques. Abstract We present a distributed parallel prover for propositional satisfiability (SAT), called PSATO, for networks of workstations. PSATO is based on the sequential SAT prover SATO, which is an efficient implementation of the Davis –Putnam algorithm. The master–slave model is used for communication. A simple and effective workload balancing method distributes the workload among workstations. A key property of our method is that the concurrent processes explore disjoint portions of the search space. In this way, we use parallelism without introducing redundant search. Our approach provides solutions to the problems of (i) cumulating intermediate results of separate runs of reasoning programs; (ii) designing highly scalable parallel algorithms and (iii) supporting “fault-tolerant” distributed computing. Several dozens of open problems in the study of quasigroups have been solved using PSATO. We also show how a useful technique called the cyclic group construction has been coded in propositional logic.