The satissability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer-aided design, computer-aided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, co...

Contemporary satisfiability solvers are the corner-stone of many successful applications in domains such as automated verification and artificial intelligence. The impressive advances of SAT solvers, achieved by clever engineering and sophisticated algorithms, enable us to tackle Boolean Satisfiability (SAT) problem instances with millions of variables – which was previously conceived as a hope...

Adversarial SAT (AdSAT) is a generalization of the satisfiability (SAT) problem in which two players try to make a boolean formula true (resp. false) by controlling their respective sets of variables. AdSAT belongs to a higher complexity class in the polynomial hierarchy than SAT and therefore the nature of the critical region and the transition are not easily paralleled to those of SAT and wor...

In computational complexity theory, a decision problem is NP-complete when it is both in NP and NP-hard. Although a solution to a NP-complete can be verified quickly, there is no known algorithm to solve it in polynomial time. There exists a method to reduce a SAT (Satifiability) problem to Subset Sum Problem (SSP) in the literature, however, it can only be applied to small or medium size probl...

The satisfiability (SAT) problem is a core, problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer-aided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, c...

The representation of Job Shop Scheduling Problem (JSSP) as the well known Satisfiabilty Problem (SAT) is useful because it helps to find feasible schedules in an efficient way. One of the most efficient SAT codifications of JSSP is RSF (Reduced Sat Codification) which transforms any JSSP instance to a 3-SAT problem. In this paper RSF is improved by codifying JSSP as 1-SAT problem by applying a...

Boolean Satisfiability (SAT) has seen many successful applications in various fields such as Electronic Design Automation and Artificial Intelligence. However, in some cases, it may be required/preferable to use variations of the general SAT problem. In this paper, we consider one important variation, the Partial MAX-SAT problem. Unlike SAT, Partial MAX-SAT has certain constraints (clauses) tha...

The satissability (SAT) problem is a basic problem in computing theory. Presently, an active area of research on SAT problem is to design eecient optimization algorithms for nding a solution for a satissable CNF formula. A new formulation, the Universal SAT problem model, which transforms the SAT problem on Boolean space into an optimization problem on real space has been developed 31, 35, 34, ...

In this paper, we propose a new approach for solving the SAT problem. This approach consists in representing SAT instances thanks to an undirected graph issued from a polynomial transformation from SAT to the CLIQUE problem. Considering this graph, we exploit well known properties of chordal graphs to manipulate the SAT instance. Firstly, these properties allow us to define a new class of SAT p...