Probabilistic approach to the satisfiability problem

On the Probabilistic Approach to the Random Satisfiability Problem

In this note I will review some of the recent results that have been obtained in the probabilistic approach to the random satisfiability problem. At the present moment the results are only heuristic. In the case of the random 3-satisfiability problem a phase transition from the satisfiable to the unsatisfiable phase is found at α = 4.267. There are other values of α that separates different reg...

A Probabilistic Approach to the Dichotomy Problem

Probabilistic performance of a heuristic for the satisfiability problem

An algorithm for the Satis ability problem is presented and its probabilistic behavior is analysed when combined with two other algorithms studied earlier. The analysis is based on an instance distribution which is parameterized to simulate a variety of sample characteristics. The algorithm dynamically assigns values to literals appearing in a given instance until a satisfying assignment is fou...

Genetic-fuzzy approach to the Boolean satisfiability problem

Witold Pedrycz, Giancarlo Succi, and Ofer Shai Owing to the immense size of the search space in the SAT problem, evolutionary computing arises as a viable and attractive option. The objective of this study is to formulate the SAT problem in the evolutionary setting and carry out comprehensive xperimental studies. The approach relies on the embedding principle: we generalize the Boolean problem ...

Probabilistic Estimates for the Generalized Maximum Satisfiability Problem

The generalized maximum satisfiability problem (GMAXSAT) deals with variables taking their values in a finite set. A set of logical clauses is given and the goal is to find an assignment of values to the variables, minimizing the number j3 of unsatisfied clauses. For randomly generated instances of a uniform type we study the distribution of p, as well as the distribution of the maximal size a ...