Maxwell-Boltzmann and Bose-Einstein Distributions for the SAT Problem

Recent studies in theoretical computer science have exploited new algorithms and methodologies based on statistical physics for investigating the structure and the properties of the Satisfiability problem. We propose a characterization of the SAT problem as a physical system, using both quantum and classical statistical-physical models. We associate a graph to a SAT instance and … Read more

Semidefinite Optimization Approaches for Satisfiability and Maximum-Satisfiability Problems

Semidefinite optimization, commonly referred to as semidefinite programming, has been a remarkably active area of research in optimization during the last decade. For combinatorial problems in particular, semidefinite programming has had a truly significant impact. This paper surveys some of the results obtained in the application of semidefinite programming to satisfiability and maximum-satisfiability problems. The … Read more

GRASP with path-relinking for the weighted maximum satisfiability problem

A GRASP with path-relinking for finding good-quality solutions of the weighted maximum satisfiability problem (MAX-SAT) is described in this paper. GRASP, or Greedy Randomized Adaptive Search Procedure, is a randomized multi-start metaheuristic, where at each iteration locally optimal solutions are constructed, each independent of the others. Previous experimental results indicate its effectiveness for solving weighted … Read more

An Improved Semidefinite Programming Relaxation for the Satisfiability Problem

The satisfiability (SAT) problem is a central problem in mathematical logic, computing theory, and artificial intelligence. An instance of SAT is specified by a set of boolean variables and a propositional formula in conjunctive normal form. Given such an instance, the SAT problem asks whether there is a truth assignment to the variables such that … Read more