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Algorithms for the Satisfiability (SAT) Problem: A Survey
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1996
"... . The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, compute ..."
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Cited by 127 (3 self)
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. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...
Interval propagation to reason about sets: definition and implementation of a practical language
 CONSTRAINTS
, 1997
"... Local consistency techniques have been introduced in logic programming in order to extend the application domain of logic programming languages. The existing languages based on these techniques consider arithmetic constraints applied to variables ranging over nite integer domains. This makes difficu ..."
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Cited by 102 (5 self)
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Local consistency techniques have been introduced in logic programming in order to extend the application domain of logic programming languages. The existing languages based on these techniques consider arithmetic constraints applied to variables ranging over nite integer domains. This makes difficult a natural and concise modelling as well as an efficient solving of a class of NPcomplete combinatorial search problems dealing with sets. To overcome these problems, we propose a solution which consists in extending the notion of integer domains to that of set domains (sets of sets). We specify a set domain by an interval whose lower and upper bounds are known sets, ordered by set inclusion. We define the formal and practical framework of a new constraint logic programming language over set domains, called Conjunto. Conjunto comprises the usual set operation symbols ([ � \ � n), and the set inclusion relation (). Set expressions built using the operation symbols are interpreted as relations (s [ s1 = s2,...). In addition, Conjunto provides us with a set of constraints called graduated constraints (e.g. the set cardinality) which map sets onto arithmetic terms. This allows us to handle optimization problems by applying a cost function to the quantifiable, i.e., arithmetic, terms which are associated to set terms. The constraint solving in Conjunto is based on local consistency techniques using interval reasoning which are extended to handle set constraints. The main contribution of this paper concerns the formal definition of the language and its design and implementation as a practical language.
CLP(R) and Some Electrical Engineering Problems
 Journal of Automated Reasoning
, 1991
"... The Constraint Logic Programming Scheme defines a class of languages designed for programming with constraints using a logic programming approach. These languages are soundly based on a unified framework of formal semantics. In particular, as an instance of this scheme with real arithmetic constrain ..."
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Cited by 35 (5 self)
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The Constraint Logic Programming Scheme defines a class of languages designed for programming with constraints using a logic programming approach. These languages are soundly based on a unified framework of formal semantics. In particular, as an instance of this scheme with real arithmetic constraints, the CLP(R) language facilitates and encourages a concise and declarative style of programming for problems involving a mix of numeric and nonnumeric computation. In this paper we illustrate the practical applicability of CLP(R) with examples of programs to solve electrical engineering problems. This field is particularly rich in problems that are complex and largely numeric, enabling us to demonstrate a number of the unique features of CLP(R). A detailed look at some of the more important programming techniques highlights the ability of CLP(R) to support wellknown, powerful techniques from constraint programming. Our thesis is that CLP(R) is an embodiment of these techniques in a langu...
Local Search for Satisfiability (SAT) Problem
, 1993
"... The satisfiability problem (SAT) is a fundamental problem in mathematical logic, constraint satisfaction, VLSI engineering, and computing theory. Methods to solve the satisfiability problem play an important role in the development of computing theory and systems. Traditional methods treat the SAT p ..."
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Cited by 33 (4 self)
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The satisfiability problem (SAT) is a fundamental problem in mathematical logic, constraint satisfaction, VLSI engineering, and computing theory. Methods to solve the satisfiability problem play an important role in the development of computing theory and systems. Traditional methods treat the SAT problem as a constrained decision problem. During past research, the number of unsatisfiable clauses as the value of an objective function was formulated. This transforms the SAT problem into a search problem  an unconstrained optimization problem to the objective function. A variety of iterative optimization techniques can be used to solve this optimization problem. In this paper, we show how to use local search techniques to solve the SAT problem. The average time complexity analysis and numerous real algorithm executions were performed. They indicate that the local search algorithms are much more efficient than the existing SAT algorithms for certain classes of conjunctive normal form (...
Global Optimization for Satisfiability (SAT) Problem
, 1994
"... The satisfiability (SAT) problem is a fundamental problem in mathematical logic, inference, automated reasoning, VLSI engineering, and computing theory. In this paper, following CNF and DNF local search methods, we introduce the Universal SAT problem model, UniSAT, that transforms the discrete SAT ..."
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Cited by 20 (3 self)
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The satisfiability (SAT) problem is a fundamental problem in mathematical logic, inference, automated reasoning, VLSI engineering, and computing theory. In this paper, following CNF and DNF local search methods, we introduce the Universal SAT problem model, UniSAT, that transforms the discrete SAT problem on Boolean space f0; 1g m into an unconstrained global optimization problem on real space E m . A direct correspondence between the solution of the SAT problem and the global minimum point of the UniSAT objective function is established. Many existing global optimization algorithms can be used to solve the UniSAT problems. Combined with backtracking /resolution procedures, a global optimization algorithm is able to verify satisfiability as well as unsatisfiability. This approach achieves significant performance improvements for certain classes of conjunctive normal form (CNF ) formulas. It offers a complementary approach to the existing SAT algorithms.
A New Perspective on Integrating Functional and Logic Languages
 Languages, Proceedings of the 3rd International Conference on Fifth Generation Computer Systems
, 1992
"... Traditionally the integration of functional and logic languages is performed by attempting to integrate their semantic logics in some way. Many languages have been developed by taking this approach, but none manages to exploit fully the programming features of both functional and logic languages and ..."
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Cited by 14 (0 self)
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Traditionally the integration of functional and logic languages is performed by attempting to integrate their semantic logics in some way. Many languages have been developed by taking this approach, but none manages to exploit fully the programming features of both functional and logic languages and provide a smooth integration of the two paradigms. We propose that improved integrated systems can be constructed by taking a broader view of the underlying semantics of logic programming. A novel integrated language paradigm, Definitional Constraint Programming (DCP), is proposed. DCP generalises constraint logic programming by admitting userdefined functions via a purely functional subsystem and enhances it with the power to solve constraints over functional programs. This constraint approach to integration results in a homogeneous unified system in which functional and logic programming features are combined naturally. 1 Introduction During the past ten years the integration of funct...
Fourier's Elimination: Which to Choose?
, 1993
"... Variable elimination is of major interest for Constraint Logic Programming Languages [JaLa86], and Constraint Query Languages [KKR90], where we would like to eliminate auxiliary variables introduced during the execution of a program. This elimination is always suitable for final results. It can also ..."
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Cited by 13 (0 self)
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Variable elimination is of major interest for Constraint Logic Programming Languages [JaLa86], and Constraint Query Languages [KKR90], where we would like to eliminate auxiliary variables introduced during the execution of a program. This elimination is always suitable for final results. It can also increase the efficiency of the intermediary processes. We focus on linear inequalities of the form ax b, where a denotes a nreal vector, x an nvector of variables, b a real number, and the juxtaposition ax denotes the inner product. In this paper, we will focus exclusively on methods related to Fourier's elimination [Fourie]. Our aim is to make visible the links between the different contributions of S.N. Cernikov [Cern63], D.A. Kolher [Kohl67], R.J. Duffin [Duff74], JL.J. Imbert [Imbe90], and J.Jaffar, M.J. Maher, P.J. Stuckey and R.H.C. Yap [JMSY92]. This study, which has never been done before, is of great interest for languages such as CHIP, CLP(!) and Prolog III. We show that the t...
Firstorder Lax Logic as a Framework for Constraint Logic Programming
, 1997
"... In this report we introduce a new prooftheoretic approach to the semantics of Constraint Logic Programming, based on an intuitionistic firstorder modal logic, called QLL. The distinguishing feature of this new approach is that the logic calculus of QLL is used not only to capture the usual exte ..."
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Cited by 12 (4 self)
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In this report we introduce a new prooftheoretic approach to the semantics of Constraint Logic Programming, based on an intuitionistic firstorder modal logic, called QLL. The distinguishing feature of this new approach is that the logic calculus of QLL is used not only to capture the usual extensional aspects of Logic Programming, i.e. "which queries are successful, " but also some of the intensional aspects, i.e. "what is the answer constraint and how is it constructed." It provides for a direct link between the modeltheoretic and the operational semantics following a formulasasprograms and proofsasconstraints principle. This approach makes use of logic in a different way than other approaches based on logic calculi. On the one side it is to be distinguished from the wellknown provability semantics which is concerned merely with what is derivable as opposed to how it is derivable, paying attention to the fact that it is the how that determines the answer constraint. ...
Logic, Optimization, and Constraint Programming
 INFORMS Journal on Computing
, 2000
"... Because of their complementary strengths, optimization and constraint programming can be profitably merged. Their integration has been the subject of increasing commercial and research activity. This paper summarizes and contrasts the characteristics of the two fields; in particular, how they use ..."
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Cited by 12 (2 self)
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Because of their complementary strengths, optimization and constraint programming can be profitably merged. Their integration has been the subject of increasing commercial and research activity. This paper summarizes and contrasts the characteristics of the two fields; in particular, how they use logical inference in di#erent ways, and how these ways can be combined. It sketches the intellectual background for recent e#orts at integration. In particular, it traces the history of logicbased methods in optimization and the development of constraint programming in artificial intelligence. It concludes with a review of recent research, with emphasis on schemes for integration, relaxation methods, and practical applications. Optimization and constraint programming are beginning to converge, despite their very di#erent origins. Optimization is primarily associated with mathematics and engineering, while constraint programming developed much more recently in the computer science an...
CUF in context
 Computational Aspects of ConstraintBased Linguistics Description. DYANA2 Deliverable
"... Introduction CUF (see [DD93]) is one amongst the current breed of typed feature logic based formalisms which are principally targeted at providing a computational system for implementing HPSG grammars. We provide a theory neutral comparison of CUF against the formalisms TFS [Zaj92][Zaj91] and ALE [ ..."
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Cited by 10 (0 self)
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Introduction CUF (see [DD93]) is one amongst the current breed of typed feature logic based formalisms which are principally targeted at providing a computational system for implementing HPSG grammars. We provide a theory neutral comparison of CUF against the formalisms TFS [Zaj92][Zaj91] and ALE [Car93] drawing out the similarities and differences. Our comparison will be concentrated mainly on the expressivity of the type system, definite clauses and control scheme which provide additional control over the SLD resolution engine. 2 Type System The HPSG grammar formalism is based around the idea of employing a (possibly extended) typed feature language for the representation of grammatical knowledge. This is a departure from the rule based approach of other grammar formalisms such as GPSG in which context free rules play a major part in grammar specification. This means that in HPSG possibly recursive type definit