Fix a set S ⊆ {0, 1}∗ of exponential size, e.g. |S ∩ {0, 1}n| ∈ Ω(αn), α > 1. The S-SAT problem asks whether a propositional formula F over variables v1, . . . , vn has a satisfying assignment (v1, . . . , vn) ∈ {0, 1}n ∩S. Our interest is in determining the complexity of S-SAT. We prove that S-SAT is NP-complete for all context-free sets S. Furthermore, we show that if S-SAT is in P for some e...

Propositional model counting or #SAT is the problem of computing the number of models for a given propositional formula, i.e., the number of distinct truth assignments to variables for which the formula evaluates to true. For a proposi-tional formula F , we will use #F to denote the model count of F. This problem is also referred to as the solution counting problem for SAT. It generalizes SAT a...

On the one hand, Constraint Satisfaction Problems allow one to declaratively model problems. On the other hand, propositional satisfiability problem (SAT) solvers can handle huge SAT instances. We thus present a technique to declaratively model set constraint problems and to encode them automatically into SAT instances. We apply our technique to the Social Golfer Problem and we also use it to b...

We consider the ~ATISFIABILITY problem (~-SAT): Given a family F of n clauses cl, ._, , c, in conjunctive normal form, each consisting of k literals corresponding to k different variables of a set of r 2 k 2 1 boolean variables, is F satisfiable? By k-SAT@ no) we denote the k-SAT problem restricted to families with n > n,(r) clauses. We prove that for each k > 3 and each integer I > 4 such that...

background and objective: magnetic resonance imaging (mri) is the most sensitive technique to detect multiple sclerosis (ms) plaques in central nervous system. in some cases, the patients who were suspected to ms, whereas mri images are normal, but whether patients don’t have ms plaques or mri images are not enough optimized enough in order to show ms plaques? the aim of the current study is ev...

A growing number of problem domains are successfully being tackled by SAT solvers. This thesis contributes to that trend by pushing the state-of-the-art of core SAT algorithms and their implementation, but also in several important application areas. It consists of five papers: the first details the implementation of the SAT solver MINISAT and the other four papers discuss specific issues relat...

. In this paper we present a new approach to solve the satisfiability problem (SAT), based on boolean networks (BN). We define a mapping between a SAT instance and a BN, and we solve SAT problem by simulating the BN dynamics. We prove that BN fixed points correspond to the SAT solutions. The mapping presented allows to develop a new class of algorithms to solve SAT. Moreover, this new approach ...

Game-SAT is a 2-player version of SAT where two players (MAX and MIN) play on a SAT instance by alternatively selecting a variable and assigning it a value true or false. MAX tries to make the formula true, while MIN tries to make it false. The Game-SAT problem is to determine the winner of a SAT instance under the rules above, assuming the perfect play by both players. The Game-SAT problem, or...

The Test Suite Minimization problem in regression testing is a software engineering problem which consists in selecting a set of test cases from a large test suite that satisfies a given condition, like maximizing the coverage and/or minimizing the oracle cost. In this work we use an approach based on SAT solvers to find optimal solutions for the Test Suite Minimization Problem. The approach co...

Boolean Satisfiability (SAT) is arguably the archetypical NP-complete decision problem. Progress in SAT solving algorithms has motivated an ever increasing number of practical applications in recent years. However, many practical uses of SAT involve solving function as opposed to decision problems. Concrete examples include computing minimal unsatisfiable subsets, minimal correction subsets, pr...