Local Search for Unsatisfiability

Local search is widely applied to satisfiable SAT problems, and on some classes outperforms backtrack search. An intriguing challenge posed by Selman, Kautz and McAllester in 1997 is to use it instead to prove unsatisfiability. We investigate two distinct approaches. Firstly we apply standard local search to a reformulation of the problem, such that a solution to the reformulation corresponds to a refutation of the original problem. Secondly we design a greedy randomised resolution algorithm that will eventually discover proofs of any size while using bounded memory. We show experimentally that both approaches can refute some problems more quickly than backtrack search.

[1]  Eli Ben-Sasson,et al.  Near Optimal Separation Of Tree-Like And General Resolution , 2004, Comb..

[2]  Michael Alekhnovich,et al.  Resolution is not automatizable unless W[P] is tractable , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[3]  Michael Alekhnovich,et al.  Resolution Is Not Automatizable Unless W[P] Is Tractable , 2008, SIAM J. Comput..

[4]  Barry Richards,et al.  Nonsystematic Search and No-Good Learning , 2000, Journal of Automated Reasoning.

[5]  Joao Marques-Silva,et al.  Using Randomization and Learning to Solve Hard Real-World Instances of Satisfiability , 2000, CP.

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

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

[8]  Bart Selman,et al.  Boosting Combinatorial Search Through Randomization , 1998, AAAI/IAAI.

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

[10]  Jacobo Torán,et al.  Space Bounds for Resolution , 1999, STACS.

[11]  Holger H. Hoos,et al.  Scaling and Probabilistic Smoothing: Efficient Dynamic Local Search for SAT , 2002, CP.

[12]  Inês Lynce,et al.  Random backtracking in backtrack search algorithms for satisfiability , 2007, Discret. Appl. Math..

[13]  Jun Gu,et al.  Efficient local search for very large-scale satisfiability problems , 1992, SGAR.

[14]  Bart Selman,et al.  Finding Small Unsatisfiable Cores to Prove Unsatisfiability of QBFs , 2006, ISAIM.

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

[16]  Holger H. Hoos,et al.  Using Stochastic Local Search to Solve Quantified Boolean Formulae , 2003, CP.

[17]  Eli Ben-Sasson,et al.  Short proofs are narrow—resolution made simple , 2001, JACM.

[18]  Patrick Prosser,et al.  SAT Encodings of the Stable Marriage Problem with Ties and Incomplete Lists , 2002 .

[19]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[20]  Chu Min Li,et al.  Look-Ahead Versus Look-Back for Satisfiability Problems , 1997, CP.

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

[22]  Lakhdar Sais,et al.  Boosting Systematic Search by Weighting Constraints , 2004, ECAI.

[23]  David A. McAllester,et al.  GSAT and Dynamic Backtracking , 1994, KR.

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

[25]  Bart Selman,et al.  Ten Challenges Redux: Recent Progress in Propositional Reasoning and Search , 2003, CP.

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

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

[28]  Wolfgang Küchlin,et al.  Formal methods for the validation of automotive product configuration data , 2003, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.