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231
Planning as satisfiability
 IN ECAI92
, 1992
"... We develop a formal model of planning based on satisfiability rather than deduction. The satis ability approach not only provides a more flexible framework for stating di erent kinds of constraints on plans, but also more accurately reflects the theory behind modern constraintbased planning systems ..."
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Cited by 431 (26 self)
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We develop a formal model of planning based on satisfiability rather than deduction. The satis ability approach not only provides a more flexible framework for stating di erent kinds of constraints on plans, but also more accurately reflects the theory behind modern constraintbased planning systems. Finally, we consider the computational characteristics of the resulting formulas, by solving them with two very different satisfiability testing procedures.
Partial Constraint Satisfaction
, 1992
"... . A constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed. In some cases it may be impossible or impractical to solve these problems completely. We may seek to partially solve the problem, in particular by satisfying ..."
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Cited by 427 (23 self)
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. A constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed. In some cases it may be impossible or impractical to solve these problems completely. We may seek to partially solve the problem, in particular by satisfying a maximal number of constraints. Standard backtracking and local consistency techniques for solving constraint satisfaction problems can be adapted to cope with, and take advantage of, the differences between partial and complete constraint satisfaction. Extensive experimentation on maximal satisfaction problems illuminates the relative and absolute effectiveness of these methods. A general model of partial constraint satisfaction is proposed. 1 Introduction Constraint satisfaction involves finding values for problem variables subject to constraints on acceptable combinations of values. Constraint satisfaction has wide application in artificial intelligence, in areas ranging from temporal r...
GSAT and Dynamic Backtracking
 Journal of Artificial Intelligence Research
, 1994
"... There has been substantial recent interest in two new families of search techniques. One family consists of nonsystematic methods such as gsat; the other contains systematic approaches that use a polynomial amount of justification information to prune the search space. This paper introduces a new te ..."
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Cited by 360 (14 self)
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There has been substantial recent interest in two new families of search techniques. One family consists of nonsystematic methods such as gsat; the other contains systematic approaches that use a polynomial amount of justification information to prune the search space. This paper introduces a new technique that combines these two approaches. The algorithm allows substantial freedom of movement in the search space but enough information is retained to ensure the systematicity of the resulting analysis. Bounds are given for the size of the justification database and conditions are presented that guarantee that this database will be polynomial in the size of the problem in question. 1 INTRODUCTION The past few years have seen rapid progress in the development of algorithms for solving constraintsatisfaction problems, or csps. Csps arise naturally in subfields of AI from planning to vision, and examples include propositional theorem proving, map coloring and scheduling problems. The probl...
The Computational Complexity of Propositional STRIPS Planning
 Artificial Intelligence
, 1994
"... I present several computational complexity results for propositional STRIPS planning, i.e., STRIPS planning restricted to ground formulas. Different planning problems can be defined by restricting the type of formulas, placing limits on the number of pre and postconditions, by restricting negation ..."
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Cited by 299 (3 self)
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I present several computational complexity results for propositional STRIPS planning, i.e., STRIPS planning restricted to ground formulas. Different planning problems can be defined by restricting the type of formulas, placing limits on the number of pre and postconditions, by restricting negation in pre and postconditions, and by requiring optimal plans. For these types of restrictions, I show when planning is tractable (polynomial) and intractable (NPhard) . In general, it is PSPACEcomplete to determine if a given planning instance has any solutions. Extremely severe restrictions on both the operators and the formulas are required to guarantee polynomial time or even NPcompleteness. For example, when only ground literals are permitted, determining plan existence is PSPACEcomplete even if operators are limited to two preconditions and two postconditions. When definite Horn ground formulas are permitted, determining plan existence is PSPACEcomplete even if operators are limited t...
Improvements To Propositional Satisfiability Search Algorithms
, 1995
"... ... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400variable 3SAT problems in about 2 hours on the average. In general, it can solve hard nvariable ..."
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Cited by 161 (0 self)
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... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400variable 3SAT problems in about 2 hours on the average. In general, it can solve hard nvariable random 3SAT problems with search trees of size O(2 n=18:7 ). In addition to justifying these claims, this dissertation describes the most significant achievements of other researchers in this area, and discusses all of the widely known general techniques for speeding up SAT search algorithms. It should be useful to anyone interested in NPcomplete problems or combinatorial optimization in general, and it should be particularly useful to researchers in either Artificial Intelligence or Operations Research.
Knowledge compilation and theory approximation
 Journal of the ACM
, 1996
"... Computational efficiency is a central concern in the design of knowledge representation systems. In order to obtain efficient systems, it has been suggested that one should limit the form of the statements in the knowledge base or use an incomplete inference mechanism. The former approach is often t ..."
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Cited by 157 (5 self)
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Computational efficiency is a central concern in the design of knowledge representation systems. In order to obtain efficient systems, it has been suggested that one should limit the form of the statements in the knowledge base or use an incomplete inference mechanism. The former approach is often too restrictive for practical applications, whereas the latter leads to uncertainty about exactly what can and cannot be inferred from the knowledge base. We present a third alternative, in which knowledge given in a general representation language is translated (compiled) into a tractable form — allowing for efficient subsequent query answering. We show how propositional logical theories can be compiled into Horn theories that approximate the original information. The approximations bound the original theory from below and above in terms of logical strength. The procedures are extended to other tractable languages (for example, binary clauses) and to the firstorder case. Finally, we demonstrate the generality of our approach by compiling concept descriptions in a general framebased language into a tractable form.
Towards an understanding of hillclimbing procedures for SAT
 In Proceedings of AAAI93
, 1993
"... Recently several local hillclimbing procedures for propositional satisability havebeen proposed, which are able to solve large and di cult problems beyond the reach ofconventional algorithms like DavisPutnam. By the introduction of some new variants of these procedures, we provide strong experimen ..."
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Cited by 137 (6 self)
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Recently several local hillclimbing procedures for propositional satisability havebeen proposed, which are able to solve large and di cult problems beyond the reach ofconventional algorithms like DavisPutnam. By the introduction of some new variants of these procedures, we provide strong experimental evidence to support the conjecture that neither greediness nor randomness is important in these procedures. One of the variants introduced seems to o er signi cant improvements over earlier procedures. In addition, we investigate experimentally how their performance depends on their parameters. Our results suggest that runtime scales less than simply exponentially in the problem size. 1
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...
Heuristics based on unit propagation for satisfiability problems
, 1997
"... The paper studies new unit propagation based heuristics for DavisPutnamLoveland (DPL) procedure. These are the novel combinations of unit propagation and the usual "Maximum Occurrences in clauses of Minimum Size " heuristics. Based on the experimental evaluations of di erent alternatives ..."
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Cited by 121 (10 self)
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The paper studies new unit propagation based heuristics for DavisPutnamLoveland (DPL) procedure. These are the novel combinations of unit propagation and the usual "Maximum Occurrences in clauses of Minimum Size " heuristics. Based on the experimental evaluations of di erent alternatives a new simple unit propagation based heuristic is put forward. This compares favorably with the heuristics employed in the current stateoftheart DPL implementations (CSAT, Tableau, POSIT). 1
The Constrainedness of Search
 In Proceedings of AAAI96
, 1999
"... We propose a definition of `constrainedness' that unifies two of the most common but informal uses of the term. These are that branching heuristics in search algorithms often try to make the most "constrained" choice, and that hard search problems tend to be "critically constrained". Our definition ..."
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Cited by 117 (26 self)
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We propose a definition of `constrainedness' that unifies two of the most common but informal uses of the term. These are that branching heuristics in search algorithms often try to make the most "constrained" choice, and that hard search problems tend to be "critically constrained". Our definition of constrainedness generalizes a number of parameters used to study phase transition behaviour in a wide variety of problem domains. As well as predicting the location of phase transitions in solubility, constrainedness provides insight into why problems at phase transitions tend to be hard to solve. Such problems are on a constrainedness "knifeedge", and we must search deep into the problem before they look more or less soluble. Heuristics that try to get off this knifeedge as quickly as possible by, for example, minimizing the constrainedness are often very effective. We show that heuristics from a wide variety of problem domains can be seen as minimizing the constrainedness (or proxies ...