Solutions for Hard and Soft Constraints Using Optimized Probabilistic Satisfiability

  • Marcelo Finger
  • Ronan Le Bras
  • Carla P. Gomes
  • Bart Selman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7962)


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.


Column Generation Soft Constraint Hard Constraint Truth Assignment Linear Restriction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Marcelo Finger
    • 1
  • Ronan Le Bras
    • 1
  • Carla P. Gomes
    • 1
  • Bart Selman
    • 1
  1. 1.Department of Computer ScienceCornell UniversityUSA

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