Propositional model counting (#SAT), i.e., counting the number of satisfying assignments of a propositional formula, is a problem of significant theoretical and practical interest. Due to the inherent complexity of the problem, approximate model counting, which counts the number of satisfying assignments to within given tolerance and confidence level, was proposed as a practical alternative to ...

In the last decade, the power of the state-of-the-art SAT and ILP (Integer Linear Programming) solvers has dramatically increased. They implement many new techniques and heuristics and since any NP problem can be converted to SAT or ILP instance, we could take advantage of these techniques in general by converting the instance of NP problem to SAT formula or Integer program. Cook-Levin theorem ...

The satisfiability problem (SAT) is a well studied problem in logic which searches for a truth assignment of a set of Boolean variables that evaluates a specific formula to true. The bandwidth minimization problem for graphs (BMPG) is a well studied problem in graphs and requires finding the labels of the nodes of a graph such that the maximum absolute difference among neighbors is minimized. T...

In this paper, we introduce a new problem, called Top-k SAT, that consists in enumerating the Top-k models of a propositional formula. A Top-k model is defined as a model with less than k models preferred to it with respect to a preference relation. We show that Top-k SAT generalizes two well-known problems: the partial Max-SAT problem and the problem of computing minimal models. Moreover, we p...

Many Integer Linear Programming (ILP) problems contain significant subproblems exclusively composed of 0-1 (binary) variables. Much effort has gone in to special solvers for 0-1 ILP, as well as specialized versions of 0-1 ILP. The boolean satisfiability problem (SAT), is fundamental to many fields, including Artificial Intelligence, Formal Verification, and Computer Aided Design, and can be vie...

Satisfiability of boolean formulas (SAT) is an interesting problem for many reasons. It was the first problem proved to be NP-complete by Cook. Efficient SAT solvers have many applications. In fact, there is a huge literature on SAT, and its connections with other optimization problems have been explored. In this paper, we look at SAT using linear algebra, a basic and fundamental mathematics th...

Presenter: Pingyu Zhang Scribe: Wesley Botham Paper: Constraint Models for the Covering Test Problem Authors: Brahim Hnich, Steven D. Prestwich, Evgeny Selensky, Barbara M. Smith, Constraints 2006 The speaker stated that the paper 1. Addresses the covering test problem, an optimization problem. 2. Models & solves the problem as a CSP and as a SAT, and 3. Discusses the performance of the approac...

In this paper we show that the problem of the existence of a p-optimal proof system for SAT can be characterized in a similar manner as J. Hartmanis and L. Hemachandra characterized the problem of the existence of complete languages for UP. Namely, there exists a p-optimal proof system for SAT if and only if there is a suitable recursive presentation of the class of all easy (polynomial time re...

In this work we propose a method for computing a minimum size training set consistent subset for the Nearest Neighbor rule (also said CNN problem) via SAT encodings. We introduce the SAT–CNN algorithm, which exploits a suitable encoding of the CNN problem in a sequence of SAT problems in order to exactly solve it, provided that enough computational resources are available. Comparison of SAT–CNN...

Many practical problems in multiple fields can be converted to a SAT problem, or a sequence of SAT problems, such that their solution immediately implies a solution to the original problem. Despite the enormous progress achieved over the last decade in the development of SAT solvers, there is strong demand for higher algorithm efficiency to solve harder and larger problems. The widespread avail...