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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...
Statespace Planning by Integer Optimization
 In Proceedings of the Sixteenth National Conference on Artificial Intelligence
, 1999
"... This paper describes ILPPLAN, a framework for solving AI planning problems represented as integer linear programs. ILPPLAN extends the planning as satisfiability framework to handle plans with resources, action costs, and complex objective functions. We show that challenging planning problems can ..."
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Cited by 59 (0 self)
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This paper describes ILPPLAN, a framework for solving AI planning problems represented as integer linear programs. ILPPLAN extends the planning as satisfiability framework to handle plans with resources, action costs, and complex objective functions. We show that challenging planning problems can be effectively solved using both traditional branchand bound IP solvers and efficient new integer local search algorithms. ILPPLAN can find better quality solutions for a set of hard benchmark logistics planning problems than had been found by any earlier system. 1 Introduction In recent years the AI community witnessed the unexpected success of satisfiability testing as a method for solving statespace planning problems (Weld 1999). Kautz and Selman (1996) demonstrated that in certain computationally challenging domains, the approach of axiomatizing problems in propositional logic and solving them with general randomized SAT algorithms (SATPLAN) was competitive with or superior to the ...
On the Use of Integer Programming Models in AI Planning
 In Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
, 1999
"... Recent research has shown the promise of using propositional reasoning and search to solve AI planning problems. In this paper, we further explore this area by applying Integer Programming to solve AI planning problems. The application of Integer Programming to AI planning has a potentially si ..."
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Cited by 45 (1 self)
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Recent research has shown the promise of using propositional reasoning and search to solve AI planning problems. In this paper, we further explore this area by applying Integer Programming to solve AI planning problems. The application of Integer Programming to AI planning has a potentially significant advantage, as it allows quite naturally for the incorporation of numerical constraints and objectives into the planning domain. Moreover, the application of Integer Programming to AI planning addresses one of the challenges in propositional reasoning posed by Kautz and Selman, who conjectured that the principal technique used to solve Integer Programsthe linear programming (LP) relaxationis not useful when applied to propositional search. We discuss various IP formulations for the class of planning problems based on STRIPSstyle planning operators. Our main objective is to show that a carefully chosen IP formulation significantly improves the "strength" of the LP relaxation, and that the resultant LPs are useful in solving the IP and the associated planning problems. Our results clearly show the importance of choosing the "right" representation, and more generally the promise of using Integer Programming techniques in the AI planning domain. 1
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 ...
Mixed Logical/Linear Programming
 Discrete Applied Mathematics
, 1996
"... Mixed logical/linear programming (MLLP) is an extension of mixed integer/linear programming (MILP). It represents the discrete elements of a problem with logical propositions and provides a more natural modeling framework than MILP. It can also have computational advantages, partly because it elimin ..."
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Cited by 33 (10 self)
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Mixed logical/linear programming (MLLP) is an extension of mixed integer/linear programming (MILP). It represents the discrete elements of a problem with logical propositions and provides a more natural modeling framework than MILP. It can also have computational advantages, partly because it eliminates integer variables when they serve no purpose, provides alternatives to the traditional continuous relaxation, and applies logic processing algorithms. This paper surveys previous work and attempts to organize ideas associated with MLLP, some old and some new, into a coherent framework. It articulates potential advantages and disadvantages of MLLP and illustrates some of them with computational experiments. 1 Introduction Mixed logical/linear programming (MLLP) is a general approach to formulating and solving optimization problems that have both discrete and continuous elements. Mixed integer/linear programming (MILP), the traditional approach, is effective in many instances. But it unn...
Solving the Incremental Satisfiability Problem
 Journal of Logic Programming
, 1992
"... Given a set of clauses in propositional logic that have been found satisfiable, we wish to check whether satisfiability is preserved when the clause set is incremented with a new clause. We describe an efficient implementation of the DavisPutnamLoveland algorithm for checking satisfiability of ..."
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Cited by 31 (6 self)
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Given a set of clauses in propositional logic that have been found satisfiable, we wish to check whether satisfiability is preserved when the clause set is incremented with a new clause. We describe an efficient implementation of the DavisPutnamLoveland algorithm for checking satisfiability of the original set. We then show how to modify the algorithm for efficient solution of the incremental problem, which is NPcomplete. We also report computational results. Suppose that a given proposition does not follow from a knowledge base encoded in propositional logic. This can be checked by adding the proposition 's denial to the knowledge base and verifying that the resulting set of propositions is satisfiable. We wish to determine whether the proposition follows when the knowledge base is augmented by one or more new propositions. Rather than resolve the satisfiability problem from scratch, we propose to use information gained while solving the original problem, so as to speed the...
Petri Net Supervisors for DES with Uncontrollable and Unobservable Transitions
 IEEE Transactions on Automatic Control
, 1999
"... A supervisor synthesis technique for Petri net plants with uncontrollable and unobservable transitions that enforces the conjunction of a set of linear inequalities on the reachable markings of the plant is presented. The approach is based on the concept of Petri net place invariants. Each step o ..."
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Cited by 30 (11 self)
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A supervisor synthesis technique for Petri net plants with uncontrollable and unobservable transitions that enforces the conjunction of a set of linear inequalities on the reachable markings of the plant is presented. The approach is based on the concept of Petri net place invariants. Each step of the procedure is illustrated through a running example involving the supervision of a robotic assembly cell. The controller is described by an auxiliary Petri net connected to the plant's transitions, providing a unified Petri net model of the closed loop system. The synthesis technique is based on the concept of admissible constraints. An inadmissible constraint can not be directly enforced on a plant due to the uncontrollability or unobservability of certain plant transitions. Procedures are given for identifying all admissible linear constraints for a plant with uncontrollable and unobservable transitions, as well as methods for transforming inadmissible constraints into admissib...
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.
Satisfiability Solvers
, 2008
"... The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worstcase exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and h ..."
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Cited by 24 (0 self)
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The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worstcase exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and hardware verification [29–31, 228], automatic test pattern generation [138, 221], planning [129, 197], scheduling [103], and even challenging problems from algebra [238]. Annual SAT competitions have led to the development of dozens of clever implementations of such solvers [e.g. 13,
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.