A New Approach to Model Counting
We introduce ApproxCount, an algorithm that approximates the number of satisfying assignments or models of a formula in propositional logic. Many AI tasks, such as calculating degree of belief and reasoning in Bayesian networks, are computationally equivalent to model counting. It has been shown that model counting in even the most restrictive logics, such as Horn logic, monotone CNF and 2CNF, is intractable in the worst-case. Moreover, even approximate model counting remains a worst-case intractable problem. So far, most practical model counting algorithms are based on backtrack style algorithms such as the DPLL procedure. These algorithms typically yield exact counts but are limited to relatively small formulas. Our ApproxCount algorithm is based on SampleSat, a new algorithm that samples from the solution space of a propositional logic formula near-uniformly. We provide experimental results for formulas from a variety of domains. The algorithm produces good estimates for formulas much larger than those that can be handled by existing algorithms.
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- 1.Bayardo Jr., R.J., Pehoushek, J.D.: Counting Models Using Connected Components. In: Proc. AAAI 2000 (2000)Google Scholar
- 3.Darwiche, A.: A Compiler for Deterministic, Decomposable Negation Normal Form. In: Proc. AAAI 2002 (2002)Google Scholar
- 8.Kautz, H., Selman, B.: Planning as Satisfiability. In: Proceedings ECAI 1992 (1992)Google Scholar
- 9.Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Engineering a Highly Efficient SAT Solver. In: 38th Design Autom. Conference, DAC 2001 (2001)Google Scholar
- 10.Papadimitriou, C.H.: On Selecting a Satisfying Truth Assignment. In: Proceedings of the Conference on the Foundations of Computer Science, pp. 163–169 (1991)Google Scholar
- 12.Sang, T., Bacchus, F., Beame, P., Kautz, H., Pitassi, T.: Combining Component Caching and Clause Learning for Effective Model Counting. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542. Springer, Heidelberg (2005)Google Scholar
- 13.Selman, B., Kautz, H., Cohen, B.: Local Search Strategies for Satisfiability Testing. In: 2nd DIMACS Challenge on Cliques, Coloring and Satisfiability (1994)Google Scholar
- 17.Wei, W., Erenrich, J., Selman, B.: Towards Efficient Sampling: Exploiting Random Walk Strategies. In: Proc. AAAI 2004 (2004)Google Scholar
- 19.SAT Competition, http://www.satcompetition.org