DPLL with Caching: A new algorithm for #SAT and Bayesian Inference

Bayesian inference and counting satisfying assignments are important problems with numerous applications in probabilistic reasoning. In this paper, we show that plain old DPLL equipped with memoization can solve both of these problems with time complexity that is at least as good as all known algorithms. Furthermore, DPLL with memoization achieves the best known time-space tradeoff. Although their worst case time complexity is no better, our DPLL based algorithms have the potential to achieve much better performance than known algorithms on problems which possess additional structure. Probabilistic models of real situations tend to have such additional structure. Electronic Colloquium on Computational Complexity, Report No. 3 (2003)

[1]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[2]  Leslie G. Valiant,et al.  The Complexity of Enumeration and Reliability Problems , 1979, SIAM J. Comput..

[3]  Paul D. Seymour,et al.  Graph minors. X. Obstructions to tree-decomposition , 1991, J. Comb. Theory, Ser. B.

[4]  Gregory M. Provan,et al.  What is the most likely diagnosis? , 1990, UAI.

[5]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[6]  Rina Dechter,et al.  Bucket elimination: A unifying framework for probabilistic inference , 1996, UAI.

[7]  David Heckerman,et al.  Causal Independence for Knowledge Acquisition and Inference , 1993, UAI.

[8]  E. Clarke,et al.  Symbolic model checking using SAT procedures instead of BDDs , 1999, Proceedings 1999 Design Automation Conference (Cat. No. 99CH36361).

[9]  Dan Roth,et al.  On the Hardness of Approximate Reasoning , 1993, IJCAI.

[10]  Olivier Dubois,et al.  Counting the Number of Solutions for Instances of Satisfiability , 1991, Theor. Comput. Sci..

[11]  Wenhui Zhang,et al.  Number of Models and Satisfiability of Sets of Clauses , 1996, Theor. Comput. Sci..

[12]  Craig Boutilier,et al.  Context-Specific Independence in Bayesian Networks , 1996, UAI.

[13]  Leslie G. Valiant,et al.  The Complexity of Computing the Permanent , 1979, Theor. Comput. Sci..

[14]  Eliezer L. Lozinskii,et al.  The Good Old Davis-Putnam Procedure Helps Counting Models , 2011, J. Artif. Intell. Res..

[15]  Eric Vigoda,et al.  A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries , 2001, STOC '01.

[16]  Rina Dechter,et al.  Resolution versus Search: Two Strategies for SAT , 2000, Journal of Automated Reasoning.

[17]  Armin Haken,et al.  The Intractability of Resolution , 1985, Theor. Comput. Sci..

[18]  Toniann Pitassi,et al.  Simplified and improved resolution lower bounds , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[19]  Michael Alekhnovich,et al.  Satisfiability, Branch-Width and Tseitin tautologies , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[20]  Unifying Tree-decomposition Schemes for Automated Reasoning Keywords : Automated Reasoning , 2022 .

[21]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[22]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[23]  Roberto J. Bayardo,et al.  Counting Models Using Connected Components , 2000, AAAI/IAAI.

[24]  Adnan Darwiche,et al.  Recursive conditioning , 2001, Artif. Intell..

[25]  Eric Vigoda,et al.  A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries , 2004, JACM.

[26]  Toniann Pitassi,et al.  Stochastic Boolean Satisfiability , 2001, Journal of Automated Reasoning.