Heuristics for fast exact model counting

Authors:
Tian Sang;Paul Beame;Henry Kautz
Affiliations:
Computer Science and Engineering, University of Washington, Seattle, WA;Computer Science and Engineering, University of Washington, Seattle, WA;Computer Science and Engineering, University of Washington, Seattle, WA
Venue:
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Year:
2005

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Abstract

An important extension of satisfiability testing is model-counting, a task that corresponds to problems such as probabilistic reasoning and computing the permanent of a Boolean matrix. We recently introduced Cachet, an exact model-counting algorithm that combines formula caching, clause learning, and component analysis. This paper reports on experiments with various techniques for improving the performance of Cachet, including component-selection strategies, variable-selection branching heuristics, randomization, backtracking schemes, and cross-component implications. The result of this work is a highly-tuned version of Cachet, the first (and currently, only) system able to exactly determine the marginal probabilities of variables in random 3-SAT formulas with 150+ variables. We use this to discover an interesting property of random formulas that does not seem to have been previously observed.