New logical and complexity results for Signed-SAT

We define Mv-formulas as the union of the subclasses of signed CNF formulas known as regular and monosigned CNF formulas, and then define resolution calculi that are refutation complete for Mv-formulas and give new complexity results for the Horn-SAT and 2-SAT problems. Our goal is to use Mv-formulas as a constraint programming language between CSP and SAT, and solve computationally difficult combinatorial problems with efficient satisfiability solvers for Mv-formulas. The results presented in this paper provide evidence that Mv-formulas are a problem modeling language that offers a good compromise between complexity and expressive power.

[1]  Roberto J. Bayardo,et al.  Using CSP Look-Back Techniques to Solve Real-World SAT Instances , 1997, AAAI/IAAI.

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

[3]  Reiner Hähnle,et al.  Automated deduction in multiple-valued logics , 1993, International series of monographs on computer science.

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

[5]  Ramón Béjar,et al.  Solving the Round Robin Problem Using Propositional Logic , 2000, AAAI/IAAI.

[6]  Reiner Hähnle,et al.  Deduction in many-valued logics: a survey , 1997 .

[7]  J.P. Marques-Silva,et al.  Solving satisfiability in combinational circuits with backtrack search and recursive learning , 1999, Proceedings. XII Symposium on Integrated Circuits and Systems Design (Cat. No.PR00387).

[8]  Ramón Béjar,et al.  Capturing Structure with Satisfiability , 2001, CP.

[9]  Ramón Béjar,et al.  Solving Combinatorial Problems with Regular Local Search Algorithms , 1999, LPAR.

[10]  Alan M. Frisch,et al.  Solving Non-Boolean Satisfiability Problems with Stochastic Local Search: A Comparison of Encodings , 2001, Journal of Automated Reasoning.

[11]  Reiner Hähnle,et al.  Short Conjunctive Normal Forms in Finitely Valued Logics , 1994, J. Log. Comput..

[12]  Bart Selman,et al.  Domain-Independent Extensions to GSAT : Solving Large StructuredSatis ability , 1993 .

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

[14]  Ramón Béjar,et al.  A Comparison of Systematic and Local Search Algorithms for Regular CNF Formulas , 1999, ESCQARU.

[15]  Ramón Béjar,et al.  Phase Transitions in the Regular Random 3-SAT Problem , 1999, ISMIS.

[16]  Neil V. Murray,et al.  Signed Formulas: A Liftable Meta-Logic for Multiple-Valued Logics , 1993, ISMIS.

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

[18]  Bernhard Beckert,et al.  The 2-SAT problem of regular signed CNF formulas , 2000, Proceedings 30th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2000).

[19]  Reiner Hähnle,et al.  The SAT problem of signed CNF formulas , 2000 .

[20]  Randal E. Bryant,et al.  Effective use of Boolean satisfiability procedures in the formal verification of superscalar and VLIW microprocessors , 2003, J. Symb. Comput..

[21]  Reiner Hähnle,et al.  Advanced Many-Valued Logics , 2001 .

[22]  Bart Selman,et al.  Balance and Filtering in Structured Satisfiable Problems , 2001, IJCAI.

[23]  Bart Selman,et al.  Pushing the Envelope: Planning, Propositional Logic and Stochastic Search , 1996, AAAI/IAAI, Vol. 2.

[24]  Carlos Ansótegui,et al.  Bridging the Gap between SAT and CSP , 2002, CP.

[25]  Joao Marques-Silva.  Algorithms for Satisfiability in Combinational Circuits Based on Backtrack Search and Recursive Learning , 1999 .

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

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

[28]  Chu Min Li,et al.  Heuristics Based on Unit Propagation for Satisfiability Problems , 1997, IJCAI.

[29]  R. Torres,et al.  Systematic and local search algorithms for regular-SAT , 2001 .