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Constraint Logic Programming: A Survey
"... Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in differe ..."
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Cited by 774 (24 self)
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Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in different areas of applications. In this survey of CLP, a primary goal is to give a systematic description of the major trends in terms of common fundamental concepts. The three main parts cover the theory, implementation issues, and programming for applications.
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 126 (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...
Finding Hard Instances of the Satisfiability Problem: A Survey
, 1997
"... . Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case ..."
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Cited by 115 (1 self)
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. Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case complexity, the threshold phenomenon, known lower bounds for certain classes of algorithms, and the problem of generating hard instances with solutions.
Mixed Integer Programming Methods for Computing Nonmonotonic Deductive Databases
, 1994
"... Though the declarative semantics of both explicit and nonmonotonic negation in logic programs has been studied extensively, relatively little work has been done on computation and implementation of these semantics. In this paper, we study three different approaches to computing stable models of logi ..."
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Cited by 45 (8 self)
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Though the declarative semantics of both explicit and nonmonotonic negation in logic programs has been studied extensively, relatively little work has been done on computation and implementation of these semantics. In this paper, we study three different approaches to computing stable models of logic programs based on mixed integer linear programming methods for automated deduction introduced by R. Jeroslow. We subsequently discuss the relative efficiency of these algorithms. The results of experiments with a prototype compiler implemented by us tend to confirm our theoretical discussion. In contrast to resolution, the mixed integer programming methodology is both fully declarative and handles reuse of old computations gracefully. We also introduce, compare, implement, and experiment with linear constraints corresponding to four semantics for "explicit" negation in logic programs: the fourvalued annotated semantics [3], the GelfondLifschitz semantics [12], the overdetermined models ...
Decomposition of Balanced Matrices
 J. COMBINATORIAL THEORY, SER. B
, 1999
"... A 0,1 matrix is balanced if it does not contain a square submatrix of odd order with two ones per row and per column. We show that a balanced 0,1 matrix is either totally unimodular or its bipartite representation has a cutset consisting of two adjacent nodes and some of their neighbors. This resul ..."
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Cited by 29 (5 self)
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A 0,1 matrix is balanced if it does not contain a square submatrix of odd order with two ones per row and per column. We show that a balanced 0,1 matrix is either totally unimodular or its bipartite representation has a cutset consisting of two adjacent nodes and some of their neighbors. This result yields a polytime recognition algorithm for balancedness. To prove the result, we first prove a decomposition theorem for balanced 0,1 matrices that are not strongly balanced.
On Finding Solutions for Extended Horn Formulas
, 1995
"... In this note we present a simple quadratictime algorithm for solving the satisfiability problem for a special class of boolean formulas. This class properly contains the class of extended Horn formulas [1] and balanced formulas [2, 4]. Previous algorithms for these classes require testing member ..."
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Cited by 22 (4 self)
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In this note we present a simple quadratictime algorithm for solving the satisfiability problem for a special class of boolean formulas. This class properly contains the class of extended Horn formulas [1] and balanced formulas [2, 4]. Previous algorithms for these classes require testing membership in the classes. However, the problem of recognizing balanced formulas is complex, and the problem of recognizing extended Horn formulas is not known to be solvable in polynomial time. Our algorithm requires no such test for membership. Keywords: Algorithms, satisfiability, extended Horn formulas, balanced matrices, unit resolution 1 Introduction Chandru and Hooker [1] introduced the class of extended Horn formulas and showed that unit resolution alone can determine whether or not a given extended Horn formula I has a satisfying truth assignment. By repeated variable assignments and unit resolutions one can obtain a satisfying truth assignment for I. The results of [1] cannot, howev...
A Perspective on Certain Polynomial Time Solvable Classes of Satisfiability
 Discrete Applied Mathematics
, 1998
"... The scope of certain wellstudied polynomialtime solvable classes of Satisfiability is investigated relative to a polynomialtime solvable class consisting of what we call matched formulas. The class of matched formulas has not been studied in the literature, probably because it seems not to contai ..."
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Cited by 17 (2 self)
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The scope of certain wellstudied polynomialtime solvable classes of Satisfiability is investigated relative to a polynomialtime solvable class consisting of what we call matched formulas. The class of matched formulas has not been studied in the literature, probably because it seems not to contain many challenging formulas. Yet, we find that, in some sense, the matched formulas are more numerous than Horn, extended Horn, renamable Horn, qHorn, CCbalanced, or Single Lookahead Unit Resolution (SLUR) formulas. In addition, we find that relatively few unsatisfiable formulas are in any of the above classes. However, there are many unsatisfiable formulas that can be solved in polynomial time by restricting resolution so as not to generate resolvents of size greater than the number of literals in a maximum length clause. We use the wellstudied random kSAT model M(n;m;k) for generating CNF formulas with m clauses, each with k distinct literals, from n variables. We show, for all m=n ? 2...
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 13 (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...
On Some Tractable Classes in Deduction and Abduction
 Artificial Intelligence
, 2000
"... We address the identification of propositional theories for which entailment is tractable, so that every query about logical consequences of the theory can be answered in polynomial time. We map tractable satisfiability classes to tractable entailment classes, including hierarchies of tractable prob ..."
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Cited by 12 (2 self)
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We address the identification of propositional theories for which entailment is tractable, so that every query about logical consequences of the theory can be answered in polynomial time. We map tractable satisfiability classes to tractable entailment classes, including hierarchies of tractable problems; and show that some initially promising conditions for tractability of entailment, proposed by Esghi [13] and del Val [10], surprisingly only identify a subset of renamable Horn. We then consider a potential application of tractable entailment, through a reduction due to Esghi [13] of certain abduction problems to a sequence of entailment problems. Besides clarifying the range of applicability of Esghi's results from the semantic point of view, we show that the reduction can almost trivially fail to be in any of the basic tractable classes discussed in the first part of the paper. We leave open the question of how to more broadly identify tractable entailment classes, as our examples ...
Average Case Results for Satisfiability Algorithms Under the Random Clause Width Model
 Annals of Mathematics and Artificial Intelligence
, 1995
"... In the probabilistic analysis of algorithms for the Satisfiability problem, the randomclausewidth model is one of the most popular for generating random instances. This model is parameterized and it is not difficult to show that virtually the entire parameter space is covered by a collection of ..."
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Cited by 9 (1 self)
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In the probabilistic analysis of algorithms for the Satisfiability problem, the randomclausewidth model is one of the most popular for generating random instances. This model is parameterized and it is not difficult to show that virtually the entire parameter space is covered by a collection of polynomial time algorithms that find solutions to random instances with probability tending to 1 as instance size increases. But finding a collection of polynomial average time algorithms that cover the parameter space has proved much harder and such results have spanned approximately ten years. However, it can now be said that virtually the entire parameter space is covered by polynomial average time algorithms. This paper relates dominant, exploitable properties of random formulas over the parameter space to mechanisms of polynomial average time algorithms. The probabilistic discussion of such properties is new; main averagecase results over the last ten years are reviewed. 1 Intr...