A Proof-Producing CSP Solver

PCS is a CSP solver that can produce a machine-checkable deductive proof in case it decides that the input problem is unsatisfiable. The roots of the proof may be nonclausal constraints, whereas the rest of the proof is based on resolution of signed clauses, ending with the empty clause. PCS uses parameterized, constraint-specific inference rules in order to bridge between the nonclausal and the clausal parts of the proof. The consequent of each such rule is a signed clause that is 1) logically implied by the nonclausal premise, and 2) strong enough to be the premise of the consecutive proof steps. The resolution process itself is integrated in the learning mechanism, and can be seen as a generalization to CSP of a similar solution that is adopted by competitive SAT solvers.

[1]  Thomas A. Henzinger,et al.  Abstractions from proofs , 2004, POPL.

[2]  Fahiem Bacchus,et al.  Generalized NoGoods in CSPs , 2005, AAAI.

[3]  Sharad Malik,et al.  Validating SAT solvers using an independent resolution-based checker: practical implementations and other applications , 2003, 2003 Design, Automation and Test in Europe Conference and Exhibition.

[4]  Sharad Malik,et al.  Efficient conflict driven learning in a Boolean satisfiability solver , 2001, IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281).

[5]  Rina Dechter,et al.  Constraint Processing , 1995, Lecture Notes in Computer Science.

[6]  Ofer Strichman,et al.  A proof-producing CSP solver: A proof supplement , 2010 .

[7]  Matthew W. Moskewicz,et al.  CAMA: A Multi-Valued Satisfiability Solver , 2003, ICCAD.

[8]  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).

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