In this paper we present MV-SAT, which is a many-valued constraint programming language that bridges the gap between Boolean Satisfiability and Constraint Satisfaction. Our overall goal is to extend the SAT formalism with many-valued sets and deal with more compact and natural encodings, as in CSP approaches, while retaining the efficiencies of SAT solvers operating on uniform encodings. After ...

The one of the most interesting problem of discrete mathematics is the SAT (satisfiability) problem. Good way in SAT solver developing is to transform the SAT problem to the problem of continuous search of global minimums of the functional associated with the CNF. This article proves the special construction of the functional and offers to solve the system of nonlinear algebraic equation that d...

The area of Propositional Satisfiability (SAT) has been the subject of intensive research in recent years, with significant theoretical and practical contributions. From a practical perspective, a large number of very effective SAT solvers have recently been proposed, most of which based on improvements made to the original Davis-Putnam-Logemann-Loveland (DPLL) backtrack search SAT algorithm. T...

We define a generalized variant of the satisfiability problem (SAT) where each “clause” is an or -list of inequalities in n variables. The inequality satisfiability problem (I-SAT) is to find whether there exists a feasible point in <n that satisfies at least one inequality in each “clause”. We show that I-SAT is harder than SAT in that I-SAT is NP-complete even when restricted to contain only ...

USING NEURAL NETWORKS AND GENETIC ALGORITHMS AS HEURISTICS FOR NP-COMPLETE PROBLEMS William M. Spears, M.S. George Mason University, 1989 Thesis Director: Dr. Kenneth A. De Jong Paradigms for using neural networks (NNs) and genetic algorithms (GAs) to heuristically solve boolean satisfiability (SAT) problems are presented. Results are presented for two-peak and false-peak SAT problems. Since SA...

While 3-SAT is NP-hard, 2-SAT solvable in polynomial time. Austrin, Guruswami, and H\r{a}stad roved a result known as "$(2+\varepsilon)$-SAT NP-hard" [FOCS'14/SICOMP'17]. They showed that the problem of distinguishing k-CNF formulas are g-satisfiable (i.e. some assignment satisfies at least g literals every clause) from those not even 1-satisfiable NP-hard if $\frac{g}{k} < \frac{1}{2}$ P other...

Boolean SATisfiability (SAT) is an important problem in AI. SAT solvers have been effectively used in important industrial applications including automated planning and verification. In this paper, we present novel algorithms for fast SAT solving by employing two common subclause elimination (CSE) approaches. Our motivation is that modern SAT solving techniques can be more efficient on CSE-proc...

We consider the problem of generating hard instances for the Satisfying Assignment Search Problem (in short, SAT). It is not known whether SAT is difficult on average, while it has been believed that the Factorization Problem (in short, FACT) is hard on average. Thus, one can expect to generate hard-on-average instances by using a reduction from FACT to SAT. Although the asymptotically best red...

In this paper we propose the approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance one can construct different partitionings, each of them is a set of simplified versions of the original SAT instance. The effectiveness of an arbitrary part...

We consider the problem of generating hard instances for the Satisfying Assignment Search Problem (in short, SAT). It is not known whether SAT is di cult on average, while it has been believed that the Factorization Problem (in short, FACT) is hard on average. Thus, one can expect to generate hard-on-average instances by using a reduction from FACT to SAT. Although the asymptotically best reduc...