Monte-Carlo Style UCT Search for Boolean Satisfiability

In this paper, we investigate the feasibility of applying algorithms based on the Uniform Confidence bounds applied to Trees [12] to the satisfiability of CNF formulas. We develop a new family of algorithms based on the idea of balancing exploitation (depth-first search) and exploration (breadth-first search), that can be combined with two different techniques to generate random playouts or with a heuristics-based evaluation function. We compare our algorithms with a DPLL-based algorithm and with WalkSAT, using the size of the tree and the number of flips as the performance measure. While our algorithms perform on par with DPLL on instances with little structure, they do quite well on structured instances where they can effectively reuse information gathered from one iteration on the next. We also discuss the pros and cons of our different algorithms and we conclude with a discussion of a number of avenues for future work.

[1]  Thomas Stützle,et al.  SATLIB: An Online Resource for Research on SAT , 2000 .

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

[3]  Csaba Szepesvári,et al.  Bandit Based Monte-Carlo Planning , 2006, ECML.

[4]  Peter Auer,et al.  The Nonstochastic Multiarmed Bandit Problem , 2002, SIAM J. Comput..

[5]  Rita Cucchiara,et al.  AI*IA 2009: Emergent Perspectives in Artificial Intelligence, XIth International Conference of the Italian Association for Artificial Intelligence, Reggio Emilia, Italy, December 9-12, 2009, Proceedings , 2009, AI*IA.

[6]  Neil D. Lawrence,et al.  Missing Data in Kernel PCA , 2006, ECML.

[7]  Peter Auer,et al.  Finite-time Analysis of the Multiarmed Bandit Problem , 2002, Machine Learning.

[8]  David Silver,et al.  Combining online and offline knowledge in UCT , 2007, ICML '07.

[9]  Moshe Y. Vardi,et al.  Random 3-SAT and BDDs: The Plot Thickens Further , 2001, CP.

[10]  Peter Auer,et al.  UCB revisited: Improved regret bounds for the stochastic multi-armed bandit problem , 2010, Period. Math. Hung..

[11]  Hans van Maaren,et al.  Sat2000: Highlights of Satisfiability Research in the Year 2000 , 2000 .

[12]  Marco Schaerf,et al.  An Algorithm to Evaluate Quantified Boolean Formulae and Its Experimental Evaluation , 2002, Journal of Automated Reasoning.

[13]  Sylvain Gelly,et al.  Modifications of UCT and sequence-like simulations for Monte-Carlo Go , 2007, 2007 IEEE Symposium on Computational Intelligence and Games.

[14]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[15]  Devika Subramanian,et al.  Random 3-SAT: The Plot Thickens , 2000, Constraints.

[16]  Bart Selman,et al.  Applying UCT to Boolean Satisfiability , 2011, SAT.

[17]  Kevin Leyton-Brown,et al.  SATzilla: Portfolio-based Algorithm Selection for SAT , 2008, J. Artif. Intell. Res..

[18]  Andrew McCallum,et al.  Piecewise pseudolikelihood for efficient training of conditional random fields , 2007, ICML '07.

[19]  Theo Tryfonas,et al.  Frontiers in Artificial Intelligence and Applications , 2009 .

[20]  Toby Walsh,et al.  Principles and Practice of Constraint Programming — CP 2001: 7th International Conference, CP 2001 Paphos, Cyprus, November 26 – December 1, 2001 Proceedings , 2001, Lecture Notes in Computer Science.

[21]  Bart Selman,et al.  Local search strategies for satisfiability testing , 1993, Cliques, Coloring, and Satisfiability.

[22]  Alessandro Zanarini,et al.  Deriving Information from Sampling and Diving , 2009, AI*IA.

[23]  Marco Schaerf,et al.  An Algorithm to Evaluate Quantified Boolean Formulae , 1998, AAAI/IAAI.

[24]  Karem A. Sakallah,et al.  Theory and Applications of Satisfiability Testing - SAT 2011 - 14th International Conference, SAT 2011, Ann Arbor, MI, USA, June 19-22, 2011. Proceedings , 2011, SAT.