Using cross-entropy for satisfiability

This paper proposes a novel approach to SAT solving by using the cross-entropy method for optimization. It introduces an extension of the Boolean satisfiability setting to a multi-valued framework, where a probability space is induced over the set of all possible assignments. For a given formula, a cross-entropy-based algorithm (implemented in a tool named CROiSSANT) is used to find a satisfying assignment by applying an iterative procedure that optimizes an objective function correlated with the likelihood of satisfaction. We investigate a hybrid approach by employing cross-entropy as a preprocessing step to SAT solving. First CROiSSANT is run to identify the areas of the search space that are more likely to contain a satisfying assignment; this information is then given to a DPLL-based SAT solver as a partial or a complete assignment that is used to suggest variables assignments in the search. We tested our approach on a set of benchmarks, in different configurations of tunable parameters of the cross-entropy algorithm; as experimental results show, it represents a sound basis for the development of a cross-entropy-based SAT solver.

[1]  Dirk P. Kroese,et al.  Handbook of Monte Carlo Methods , 2011 .

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

[3]  Thomas Stützle,et al.  Stochastic Local Search: Foundations & Applications , 2004 .

[4]  Hector J. Levesque,et al.  A New Method for Solving Hard Satisfiability Problems , 1992, AAAI.

[5]  Bart Selman,et al.  Ten Challenges in Propositional Reasoning and Search , 1997, IJCAI.

[6]  Jonathan M. Keith,et al.  Rare event simulation and combinatorial optimization using cross entropy: sequence alignment by rare event simulation , 2002, WSC '02.

[7]  Lakhdar Sais,et al.  Learning in Local Search , 2009, 2009 21st IEEE International Conference on Tools with Artificial Intelligence.

[8]  Bart Selman,et al.  Evidence for Invariants in Local Search , 1997, AAAI/IAAI.

[9]  Toby Walsh,et al.  Towards an Understanding of Hill-Climbing Procedures for SAT , 1993, AAAI.

[10]  Bart Selman,et al.  Noise Strategies for Improving Local Search , 1994, AAAI.

[11]  Holger H. Hoos,et al.  On the Run-time Behaviour of Stochastic Local Search Algorithms for SAT , 1999, AAAI/IAAI.

[12]  Adnan Darwiche,et al.  A Lightweight Component Caching Scheme for Satisfiability Solvers , 2007, SAT.

[13]  Lakhdar Sais,et al.  Integrating Conflict Driven Clause Learning to Local Search , 2009, LSCS.

[14]  Jon Froehlich,et al.  WalkSAT as an Informed Heuristic to DPLL in SAT Solving , 2022 .

[15]  Joao Marques-Silva,et al.  Improvements to Hybrid Incremental SAT Algorithms , 2008, SAT.

[16]  Thomas Stützle,et al.  Stochastic Local Search , 2007, Handbook of Approximation Algorithms and Metaheuristics.

[17]  Panagiotis Manolios,et al.  Implementing Survey Propagation on Graphics Processing Units , 2006, SAT.

[18]  Reuven Y. Rubinstein,et al.  Optimization of computer simulation models with rare events , 1997 .

[19]  Adrian Balint,et al.  A Novel Approach to Combine a SLS- and a DPLL-Solver for the Satisfiability Problem , 2009, SAT.

[20]  Djamal Habet,et al.  A Hybrid Approach for SAT , 2002, CP.

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

[22]  Eitan Farchi,et al.  Cross-Entropy Based Testing , 2007, Formal Methods in Computer Aided Design (FMCAD'07).

[23]  Lotfi A. Zadeh,et al.  Fuzzy Logic , 2009, Encyclopedia of Complexity and Systems Science.

[25]  Joao Marques-Silva,et al.  The Impact of Branching Heuristics in Propositional Satisfiability Algorithms , 1999, EPIA.

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

[27]  Reuven Y. Rubinstein,et al.  Cross-entropy and rare events for maximal cut and partition problems , 2002, TOMC.

[28]  Dirk P. Kroese,et al.  The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning , 2004 .

[29]  Dirk P. Kroese,et al.  Application of the Cross-Entropy Method to the Buffer Allocation Problem in a Simulation-Based Environment , 2005, Ann. Oper. Res..

[30]  Lakhdar Sais,et al.  Boosting complete techniques thanks to local search methods , 1998, Annals of Mathematics and Artificial Intelligence.

[31]  Michael S. Hsiao,et al.  A new hybrid solution to boost SAT solver performance , 2007 .

[32]  Eitan Farchi,et al.  Cross-Entropy-Based Replay of Concurrent Programs , 2009, FASE.

[33]  Dirk P. Kroese,et al.  Convergence properties of the cross-entropy method for discrete optimization , 2007, Oper. Res. Lett..

[34]  Wheeler Ruml,et al.  Complete Local Search for Propositional Satisfiability , 2004, AAAI.

[35]  Edward A. Hirsch,et al.  UnitWalk: A new SAT solver that uses local search guided by unit clause elimination , 2005, Annals of Mathematics and Artificial Intelligence.

[36]  Niklas Sörensson,et al.  An Extensible SAT-solver , 2003, SAT.

[37]  Narendra Jussien,et al.  Local search with constraint propagation and conflict-based heuristics , 2000, Artif. Intell..

[38]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[39]  L. Margolin,et al.  On the Convergence of the Cross-Entropy Method , 2005, Ann. Oper. Res..

[40]  Dale Schuurmans,et al.  Local search characteristics of incomplete SAT procedures , 2000, Artif. Intell..