SAT-Solving Based on Boundary Point Elimination

We study the problem of building structure-aware SAT-solvers based on resolution. In this study, we use the idea of treating a resolution proof as a process of Boundary Point Elimination (BPE). We identify two problems of using SAT-algorithms with Conflict Driven Clause Learning (CDCL) for structure-aware SAT-solving. We introduce a template of resolution based SAT-solvers called BPE-SAT that is based on a few generic implications of the BPE concept. BPE-SAT can be viewed as a generalization of CDCL SAT-solvers and is meant for building new structure-aware SAT-algorithms. We give experimental results substantiating the ideas of the BPE approach. In particular, to show the importance of structural information we compare an implementation of BPE-SAT and state-of-the-art SAT-solvers on narrow CNF formulas.

[1]  Harald Ganzinger,et al.  Resolution Theorem Proving , 2001, Handbook of Automated Reasoning.

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

[3]  Sharad Malik,et al.  Conflict driven learning in a quantified Boolean satisfiability solver , 2002, IEEE/ACM International Conference on Computer Aided Design, 2002. ICCAD 2002..

[4]  Alan Robinson,et al.  Handbook of automated reasoning , 2001 .

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

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

[7]  Joao Marques-Silva,et al.  GRASP-A new search algorithm for satisfiability , 1996, Proceedings of International Conference on Computer Aided Design.

[8]  Rina Dechter,et al.  Directional Resolution: The Davis-Putnam Procedure, Revisited , 1994, KR.

[9]  Oliver Kullmann,et al.  Theory and Applications of Satisfiability Testing - SAT 2009, 12th International Conference, SAT 2009, Swansea, UK, June 30 - July 3, 2009. Proceedings , 2009, SAT.

[10]  Armin Biere,et al.  PicoSAT Essentials , 2008, J. Satisf. Boolean Model. Comput..

[11]  Karem A. Sakallah,et al.  GRASP—a new search algorithm for satisfiability , 1996, ICCAD 1996.

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

[13]  C. Leonard Berman,et al.  Circuit width, register allocation, and ordered binary decision diagrams , 1991, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[14]  Eugene Goldberg.  Boundary Points and Resolution , 2009, SAT.

[15]  Adnan Darwiche,et al.  On the Power of Clause-Learning SAT Solvers with Restarts , 2009, CP.

[16]  Roberto Rossi,et al.  Synthesizing Filtering Algorithms for Global Chance-Constraints , 2009, CP.

[17]  Bart Selman,et al.  Backdoors To Typical Case Complexity , 2003, IJCAI.