Solutions for hard and soft constraints using optimized probabilistic satisfiability

Authors:
Marcelo Finger;Ronan Le Bras;Carla P. Gomes;Bart Selman
Affiliations:
Department of Computer Science, Cornell University;Department of Computer Science, Cornell University;Department of Computer Science, Cornell University;Department of Computer Science, Cornell University
Venue:
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Year:
2013

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Abstract

Practical problems often combine real-world hard constraints with soft constraints involving preferences, uncertainties or flexible requirements. A probability distribution over the models that meet the hard constraints is an answer to such problems that is in the spirit of incorporating soft constraints. We propose a method using SAT-based reasoning, probabilistic reasoning and linear programming that computes such a distribution when soft constraints are interpreted as constraints whose violation is bound by a given probability. The method, called Optimized Probabilistic Satisfiability (oPSAT), consists of a two-phase computation of a probability distribution over the set of valuations of a SAT formula. Algorithms for both phases are presented and their complexity is discussed. We also describe an application of the oPSAT technique to the problem of combinatorial materials discovery.