This paper refutes the validity of the polynomial-time algorithm for solving satisfiability proposed by Sergey Gubin. Gubin introduces the algorithm using 3-SAT and eventually expands it to accept a broad range of forms of the Boolean satisfiability problem. Because 3-SAT is NP-complete, the algorithm would have implied P = NP, had it been correct. Additionally, this paper refutes the correctne...

Answer set programming (ASP) is a declarative programming paradigm for solving search problems arising in knowledge-intensive domains. One viable way to implement the computation of answer sets corresponding to problem solutions is to recast a logic program as a Boolean satisfiability (SAT) problem and to use existing SAT solver technology for the actual search. Such mappings can be obtained by...

We introduce the problem Max#SAT, an extension of model counting (#SAT). Given a formula over sets of variables X , Y , and Z, the Max#SAT problem is to maximize over the variables X the number of assignments to Y that can be extended to a solution with some assignment to Z. We demonstrate that Max#SAT has applications in many areas, showing how it can be used to solve problems in probabilistic...

Bounded Model Checking based on SAT methods has recently been introduced as a complementary technique to BDD-based Symbolic Model Checking. The basic idea is to search for a counter example in executions whose length is bounded by some integer k. The BMC problem can be e ciently reduced to a propositional satis ability problem, and can therefore be solved by SAT methods rather than BDDs. SAT pr...

Acyclicity is a recurring property of solutions to many important combinatorial problems. In this work we study embeddings of specialized acyclicity constraints in the satisfiability problem of the classical propositional logic (SAT). We propose an embedding of directed graphs in SAT, with arcs labelled with propositional variables, and an extended SAT problem in which all clauses have to be sa...

Boolean satisfiability (SAT) is the canonical NP-complete problem that plays an important role in AI and has many practical applications in Computer Science in general. Boolean networks (BN) are dynamical systems that have recently been proposed as an algorithm for solving SAT problems [7]. We have carried out a detailed investigation of the dynamical properties of BN corresponding to random SA...

Boolean Satisfiability (SAT) solvers are a mature technology to solve hard combinatorial problems. The input to a SAT solver is the problem translated to propositional logic in conjunctive normal form (CNF). This thesis studies such translations and aims to make SAT solvers more accessible to non-encoding experts.

Max-SAT resolution is the adaption of the powerful SAT resolution rule for the Max-SAT problem. One of the differences between these two rules is that Max-SAT resolution adds, besides the resolvent, several compensation clauses to keep the formula’s equivalency. We address in this paper the problem of reducing both the number and the size of these compensation clauses. We show that the order in...

MAX-SAT, the optimisation variant of the satisfiability problem in propositional logic, is an important and widely studied combinatorial optimisation problem with applications in AI and other areas of computing science. In this paper, we present a new stochastic local search (SLS) algorithm for MAXSAT that combines Iterated Local Search and Tabu Search, two well-known SLS methods that have been...

Cook [l] has shown that 3-SAT, the Boolean satisfiability problem restricted to instances with exactly three variables per clause, is NP-complete. This is a tightest possible restriction on the number of variables in a clause because as Even et al. [2] demonstrate, 2-SAT is in P. Horowitz and Sahni [5] point up the importance of finding the strongest possible restrictions under which a problem ...