The propositional satisfiability (SAT) problem is one of the most fundamental problems in computer science. SAT solvers have been successfully applied to a wide range of practical applications, including hardware model checking, software model finding, equivalence checking, and planning, among many others. Empirical research has been very fruitful for the development of efficient methods for SA...

[2] are known. In this paper, we propose a backtracking algorithm to solve MEASURE, analyze its average running time ((4) to (7) in Section 5), and show that the backtracking algorithm is more efficient than the former algorithms[1, 2] when P ƒ Q „ ‚ and there are many large hy-perrectangles ((8) and (9) in Section 6). By the way, MEASURE can be considered a generalization of the problem to cou...

This paper considers the DiversekSet problem in SAT, that is, the problem of efficiently generating a number of diverse solutions (satisfying assignments) given a propositional formula. We provide an extensive analysis of existing algorithms for this problem in a newly developed framework and propose new algorithms. While existing algorithms adapt modern SAT solvers to solve DiversekSet by chan...

Karloo and Zwick obtained recently an optimal 7=8-approximation algorithm for MAX 3-SAT. In an attempt to see whether similar methods can be used to obtain a 7=8-approximation algorithm for MAX SAT, we consider the most natural generalization of MAX 3-SAT, namely MAX 4-SAT. We present a semideenite programming relaxation of MAX 4-SAT and a new family of rounding procedures that try to cope well...

The performance of Graphics Processing Units (GPU) has increased in an impressive way in the last few years. The explosion of their computational capacity fascinates various scientific communities. However, programming style must be adapted to fully exploit this massively parallel architecture, which is not necessarily straightforward. This article proposes a first GPU approach for solving the ...

We propose an algorithm for the strengthening of the Generalized Set Covering formulation of the MAX-SAT Problem. Unlike the standard approach, our procedure does not rely on the solution of the linear relaxation to generate the cuts used to strengthen the formulation. On the contrary, it computes a La-grangian bound and uses the Lagrangian multipliers to guide the generation of cutting planes....

There are errors in the algorithm proposed by Narendra Chaudhari [2] purporting to solve the 3-sat problem in polynomial time. The present paper presents an instance for which the algorithm outputs erroneous results. Introduction: In his paper [1], Narendra Chaudhari describes an algorithm to find a solution for the 3-sat problem in polynomial time. In a second paper [2], he improves on his pre...

Analyzing the solution space structure and evolution of 3-satisfiability (3-SAT) problem is an important way to study difficulty solving satisfiability (SAT) problem. However, there no unified analysis model for spatial solutions under different constraint densities. The phase transition points regions based on metric models. 3-SAT obtained by planting strategy belief propagation. According dis...

In this paper, a cryptanalysis of the Bivium keystream generator in the SAT form is considered. For encoding the initial cryptanalysis problem into SAT a special program system TRANSALG was used. For an obtained SAT instance we use Monte Carlo method to search for a partitioning with good time estimation. Several weakened cryptanalysis instances of the Bivium generator were successfully solved ...

Due to its prominence in artificial intelligence and theoretical computer science, the propositional satisfiability problem (SAT) has received considerable attention in the past. Traditionally, this problem was attacked with systematic search algorithms, but more recently, local search methods were shown to be very effective for solving large and hard SAT instances. Especially in the light of r...