The theory of hierarchical Boolean satisfiability (SAT) solving proposed in this paper is based on a strict axiomatic system and introduces a new important notion of implicativity. The theory makes evident that increasing implicativity is the core of SAT-solving. We provide a theoretical basis for increasing the implicativity of a given SAT instance and for organizing SAT-solving in a hierarchi...

Max-SAT is an extensively studied optimization problem and variations of Max-SAT (like Partial Max-SAT and Weighted Max-SAT) can be used for computing minimal diagnoses. In this report we (1) describe a family of algorithms for computing minimal diagnoses based on Max-SAT and (2) experimentally evaluate the performance and optimality of these algorithms on a benchmark consisting of 74XXX/ISCAS8...

We establish the satisfiability threshold for random $k$-SAT all $k\ge k_0$, with $k_0$ an absolute constant. That is, there exists a limiting density $\alpha_{\rm sat}(k)$ such that formula of clause $\alpha$ is high probability satisfiable $\alpha\lt \alpha_{\rm sat}$, and unsatisfiable $\alpha>\alpha_{\rm sat}$. show given explicitly by one-step replica symmetry breaking prediction from stat...

An interesting strategy called configuration checking (CC) was recently proposed to handle the cycling problem in local search for Minimum Vertex Cover. A natural question is whether this CC also works SAT. The direct application of did not result stochastic (SLS) algorithms that can compete with current best SLS In paper, we propose a new heuristic based on SAT, which aspiration (CCA). It used...

We study the problem of building structure-aware SAT-solvers based on resolution. In this study, we use the idea of treating a resolution proof as a process of Boundary Point Elimination (BPE). We identify two problems of using SAT-algorithms with Conflict Driven Clause Learning (CDCL) for structure-aware SAT-solving. We introduce a template of resolution based SAT-solvers called BPE-SAT that i...

classifying remote sensing imageries to obtain reliable and accurate landuse/cover (luc) information still remains a challenge that depends on many factors suchas complexity of landscape especially in arid region. the aim of this paper is to extractreliable luc information from land sat imageries of the pishkouh watershed of centralarid region, iran. the classical maximum likelihood classifier ...

I discuss recent progress in developing and exploiting connections between SAT algorithms and circuit lower bounds. The centrepiece of the article is Williams’ proof that NEXP * ACC0, which proceeds via a new algorithm for ACC0-SAT beating brute-force search. His result exploits a formal connection from non-trivial SAT algorithms to circuit lower bounds. I also discuss various connections in th...

Last year when UC President Atkinson proposed discontinuing UC's use of the SAT I examination as an admissions requirement in favor of the SAT II, UCOP released several papers describing a series of studies assessing the relative predictive validity of SAT I and SAT II test scores and high school GPA on UC freshman GPA. The mediating effect of socioeconomic status (SES) was also considered. The...

SAT has become the backbone of many software systems. In order to make full use of the power of SAT solvers, a SAT compiler must encode domain variables and constraints into an efficient SAT formula. Despite many proposals for SAT encodings, there are few working SAT compilers. This paper presents Picat-SAT, the SAT compiler in the Picat system. Picat-SAT employs the sign-and-magnitude log enco...

High order Boltzmann machines (HOBM) have been proposed some time ago, but few applications have been reported. SAT is the canonical NP-complete problem. MAX-SAT is a generalization of SAT in sense that its solution provides answers to SAT. In this paper we propose a mapping on the MAX-SAT problem, in the propositional calculus setting, into HOBM combinatorial optimization problem. The approxim...