In this paper, ManySAT a new portfolio-based parallel SAT solver is thoroughly described. The design of ManySAT benefits from the main weaknesses of modern SAT solvers: their sensitivity to parameter tuning and their lack of robustness. ManySAT uses a portfolio of complementary sequential algorithms obtained through careful variations of the standard DPLL algorithm. Additionally, each sequential algorithm shares clauses to improve the overall performance of the whole system. This contrasts with most of the parallel SAT solvers generally designed using the divide-and-conquer paradigm. Experiments on many industrial SAT instances, and the first rank obtained by ManySAT in the parallel track of the 2008 SAT-Race clearly show the potential of our design philosophy.

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ManySAT: a Parallel SAT Solver

Publisher Summary The past few years have seen enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worst-case exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a general-purpose tool in areas as diverse as software and hardware verification, automatic test-pattern generation, planning, scheduling, and even challenging problems from algebra. Annual SAT competitions have led to the development of dozens of clever implementations of such solvers, exploration of new techniques, and creation of an extensive suite of real-world instances as well as challenging hand-crafted benchmark problems. Modern SAT solvers provide a black-box procedure that can often solve hard structured problems with over a million variables and several million constraints. This chapter describes the main solution techniques used in modern SAT solvers, classifying them as complete and incomplete methods. It discusses recent insights explaining the effectiveness of these techniques on practical SAT encodings and presents several extensions of the SAT approach currently under development. These extensions further expand the range of applications to include multiagent and probabilistic reasoning.

Chapter 2 Satisfiability Solvers

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.

PSATO: a distributed propositional prover and its application to quasigroup problems

Deciding the satisfiability of a Quantified Boolean Formula (QBF) is an important research issue in Artificial Intelligence. Many reasoning tasks involving planning [1], abduction, reasoning about knowledge, non monotonic reasoning [2], can be directly mapped into the problem of deciding the satisfiability of a QBF. In this paper we present QuBE, a system for deciding QBFs satisfiability.

/pdf/qube-a-system-for-deciding-quantified-boolean-formulas-2ol9vlj91c.pdf

QUBE: A System for Deciding Quantified Boolean Formulas Satisfiability

https://www.csie.ntu.edu.tw/~b92003/alcom/Backjumping%20for%20Quantified%20Boolean%20Logic%20Satisfiability.pdf

Backjumping for quantified Boolean logic satisfiability

We present a fast parallel SAT-solver on a message based MIMD machine. The input formula is dynamically divided into disjoint subformulas. Small subformulas are solved by a fast sequential SAT-solver running on every processor, which is based on the Davis-Putnam procedure with a special heuristic for variable selection. The algorithm uses optimized data structures to modify Boolean formulas. Additionally efficient workload balancing algorithms are used, to achieve a uniform distribution of workload among the processors. We consider the communication network topologiesd-dimensional processor grid and linear processor array. Tests with up to 256 processors have shown very good efficiency-values (>0.95).

Max Böhm

Papers

A fast parallel SAT-solver — efficient workload balancing