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Improvements to Propositional Satisfiability Search Algorithms, (1995)

by J W Freeman
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Chaff: Engineering an Efficient SAT Solver

by Matthew W. Moskewicz , Conor F. Madigan, Ying Zhao, Lintao Zhang, Sharad Malik , 2001
"... Boolean Satisfiability is probably the most studied of combinatorial optimization/search problems. Significant effort has been devoted to trying to provide practical solutions to this problem for problem instances encountered in a range of applications in Electronic Design Automation (EDA), as well ..."
Abstract - Cited by 1350 (18 self) - Add to MetaCart
Boolean Satisfiability is probably the most studied of combinatorial optimization/search problems. Significant effort has been devoted to trying to provide practical solutions to this problem for problem instances encountered in a range of applications in Electronic Design Automation (EDA), as well as in Artificial Intelligence (AI). This study has culminated in the development of several SAT packages, both proprietary and in the public domain (e.g. GRASP, SATO) which find significant use in both research and industry. Most existing complete solvers are variants of the Davis-Putnam (DP) search algorithm. In this paper we describe the development of a new complete solver, Chaff, which achieves significant performance gains through careful engineering of all aspects of the search – especially a particularly efficient implementation of Boolean constraint propagation (BCP) and a novel low overhead decision strategy. Chaff has been able to obtain one to two orders of magnitude performance improvement on difficult SAT benchmarks in comparison with other solvers (DP or otherwise), including GRASP and SATO.
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...Ying Zhao, Lintao Zhang, Sharad Malik Department of Electrical Engineering Princeton University {yingzhao, lintaoz, sharad}@ee.princeton.edu Many publicly available SAT solvers (e.g. GRASP [8], POSIT =-=[5]-=-, SATO [13], rel_sat [2], WalkSAT [9]) have been developed, most employing some combination of two main strategies: the Davis-Putnam (DP) backtrack search and heuristic local search. Heuristic local s...

GRASP: A search algorithm for propositional satisfiability.

by Joao P Marques-Silva, Karem A Sakallah - IEEE Transactions on Computers, , 1999
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Abstract - Cited by 479 (38 self) - Add to MetaCart
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...olean Constraint Propagation (BCP) [39] or as derivation of implications in the electronic CAD literature [1]. Most of the recently proposed improvements to the basic Davis-Putnam procedure [3], [6], =-=[11]-=-, [12], [22], [30], [36], [39] can be distinguished based on their decision making heuristics or their use of preprocessing or relaxation techniques. Common to all these approaches, however, is . J.P....

RACER system description

by Volker Haarslev, Ralf Möller , 2001
"... Abstract. RACER implements a TBox and ABox reasoner for the logic SHIQ. RACER was the first full-fledged ABox description logic system for a very expressive logic and is based on optimized sound and complete algorithms. RACER also implements a decision procedure for modal logic satisfiability proble ..."
Abstract - Cited by 452 (41 self) - Add to MetaCart
Abstract. RACER implements a TBox and ABox reasoner for the logic SHIQ. RACER was the first full-fledged ABox description logic system for a very expressive logic and is based on optimized sound and complete algorithms. RACER also implements a decision procedure for modal logic satisfiability problems (possibly with global axioms). 1
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...arantee good average-case performance. The RACER architecture incorporates the following standard optimization techniques: dependency-directed backtracking [22] and DPLL-style semantic branching (see =-=[6]-=- for an overview of the literature). Among a set of new optimization techniques, the integration of these techniques into DL reasoners for concept consistency has been described in [15]. The implement...

Extending and Implementing the Stable Model Semantics

by Patrik Simons, Ilkka Niemelä, Timo Soininen , 2002
"... A novel logic program like language, weight constraint rules, is developed for answer set programming purposes. It generalizes normal logic programs by allowing weight constraints in place of literals to represent, e.g., cardinality and resource constraints and by providing optimization capabilities ..."
Abstract - Cited by 396 (9 self) - Add to MetaCart
A novel logic program like language, weight constraint rules, is developed for answer set programming purposes. It generalizes normal logic programs by allowing weight constraints in place of literals to represent, e.g., cardinality and resource constraints and by providing optimization capabilities. A declarative semantics is developed which extends the stable model semantics of normal programs. The computational complexity of the language is shown to be similar to that of normal programs under the stable model semantics. A simple embedding of general weight constraint rules to a small subclass of the language called basic constraint rules is devised. An implementation of the language, the smodels system, is developed based on this embedding. It uses a two level architecture consisting of a front-end and a kernel language implementation. The front-end allows restricted use of variables and functions and compiles general weight constraint rules to basic constraint rules. A major part of the work is the development of an ecient search procedure for computing stable models for this kernel language. The procedure is compared with and empirically tested against satis ability checkers and an implementation of the stable model semantics. It offers a competitive implementation of the stable model semantics for normal programs and attractive performance for problems where the new types of rules provide a compact representation.

Efficient Conflict Driven Learning in a Boolean Satisfiability Solver

by Lintao Zhang, Conor F. Madigan, Matthew H. Moskewicz - In ICCAD , 2001
"... One of the most important features of current state-of-the-art SAT solvers is the use of conflict based backtracking and learning techniques. In this paper, we generalize various conflict driven learning strategies in terms of different partitioning schemes of the implication graph. We re-examine th ..."
Abstract - Cited by 348 (8 self) - Add to MetaCart
One of the most important features of current state-of-the-art SAT solvers is the use of conflict based backtracking and learning techniques. In this paper, we generalize various conflict driven learning strategies in terms of different partitioning schemes of the implication graph. We re-examine the learning techniques used in various SAT solvers and propose an array of new learning schemes. Extensive experiments with real world examples show that the best performing new learning scheme has at least a 2X speedup compared with learning schemes employed in state-of-the-art SAT solvers.
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... exists. Various EDA applications ranging from formal verification [2][3] to ATPG [1] use efficient SAT solvers as the basis for reasoning and searching. Many dedicated solvers (e.g. GRASP [6], POSIT =-=[5], S-=-ATO [8], rel_sat [7], Walksat [4], Chaff [9]) based on various algorithms (e.g. Davis Putnam [10], local search [4], Stälmark’s algorithm [11]) have been proposed to solve the SAT problem efficient...

BerkMin: a fast and robust sat-solver

by Evgueni Goldberg, Yakov Novikov , 2002
"... We describe a SAT-solver, BerkMin, that inherits such features of GRASP, SATO, and Chaff as clause recording, fast BCP, restarts, and conflict clause “aging”. At the same time BerkMin introduces a new decision making procedure and a new method of clause database management. We experimentally compare ..."
Abstract - Cited by 284 (5 self) - Add to MetaCart
We describe a SAT-solver, BerkMin, that inherits such features of GRASP, SATO, and Chaff as clause recording, fast BCP, restarts, and conflict clause “aging”. At the same time BerkMin introduces a new decision making procedure and a new method of clause database management. We experimentally compare BerkMin with Chaff, the leader among SAT-solvers used in the EDA domain. Experiments show that our solver is more robust than Chaff. BerkMin solved all the instances we used in experiments including very large CNFs from a microprocessor verification benchmark suite. On the other hand, Chaff was not able to complete some instances even with the timeout limit of 16 hours. 1.
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...esis [5], equivalence checking [6,9], and model checking [4] reduce to the satisfiability problem. In the last decade substantial progress has been made in the development of practical SAT algorithms =-=[1,2,8,11,12,13,15,18]-=-. All of them are search algorithms that aim at finding a satisfying assignment by variable splitting. Search algorithms of that kind are descendants of the DPLL-algorithm [7]. DPLL-algorithm can be c...

Using CSP look-back techniques to solve real-world SAT instances

by Roberto J. Bayardo , 1997
"... We report on the performance of an enhanced version of the “Davis-Putnam ” (DP) proof procedure for propositional satisfiability (SAT) on large instances derived from realworld problems in planning, scheduling, and circuit diagnosis and synthesis. Our results show that incorporating CSP lookback tec ..."
Abstract - Cited by 232 (1 self) - Add to MetaCart
We report on the performance of an enhanced version of the “Davis-Putnam ” (DP) proof procedure for propositional satisfiability (SAT) on large instances derived from realworld problems in planning, scheduling, and circuit diagnosis and synthesis. Our results show that incorporating CSP lookback techniques-- especially the relatively new technique of relevance-bounded learning-- renders easy many problems which otherwise are beyond DP’s reach. Frequently they make DP, a systematic algorithm, perform as well or better than stochastic SAT algorithms such as GSAT or WSAT. We recommend that such techniques be included as options in implementations of DP, just as they are in systematic algorithms for the more general constraint satisfaction problem.

Sato: An efficient propositional prover.

by H ZHANG - In Proceedings of the International Conference on Automated Deduction. Lecture Notes in Artificial Intelligence , 1997
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Abstract - Cited by 227 (6 self) - Add to MetaCart
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...r hand, a proved effective splitting rule is to choose a variable x such that the value f 2 (x)sf 2 (:x) is maximal, where f 2 (L) is one plus the number of occurrences of literal L in binary clauses =-=[2, 5]-=-. We tried to combine the above two rules into one as follows: Let 0 ! as1 and n be the number of shortest non-Horn clauses in the current set. At first, we collect all the variable names appearing in...

Practical reasoning for very expressive description logics

by Ian Horrocks - Journal of the Interest Group in Pure and Applied Logics 8 , 2000
"... Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm t ..."
Abstract - Cited by 185 (22 self) - Add to MetaCart
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm that decides satisfiability of the DL ALC extended with transitive and inverse roles and functional restrictions with respect to general concept inclusion axioms and role hierarchies; early experiments indicate that this algorithm is well-suited for implementation. Additionally, we show that ALC extended with just transitive and inverse roles is still in PSpace. We investigate the limits of decidability for this family of DLs, showing that relaxing the constraints placed on the kinds of roles used in number restrictions leads to the undecidability of all inference problems. Finally, we describe a number of optimisation techniques that are crucial in obtaining implementations of the decision procedures, which, despite the hight worst-case complexity of the problem, exhibit good performance with real-life problems. 1
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...x) that present only one expansion possibility and to detect a clash when a disjunction in (x) has no expansion possibilities. This simplification has been called boolean constraint propagation (BCP) =-=[20]-=-. In effect, the inference rule ¬C1,... ,¬Cn,C1 ⊔ ...⊔ Cn ⊔ D D Downloaded from http://jigpal.oxfordjournals.org at Serial Record on August 13, 2010 is being used to simplify the conjunctive concept r...

Constructing Conditional Plans by a Theorem-Prover

by Jussi Rintanen - Journal of Artificial Intelligence Research , 1999
"... The research on conditional planning rejects the assumptions that there is no uncertainty or incompleteness of knowledge with respect to the state and changes of the system the plans operate on. Without these assumptions the sequences of operations that achieve the goals depend on the initial sta ..."
Abstract - Cited by 155 (6 self) - Add to MetaCart
The research on conditional planning rejects the assumptions that there is no uncertainty or incompleteness of knowledge with respect to the state and changes of the system the plans operate on. Without these assumptions the sequences of operations that achieve the goals depend on the initial state and the outcomes of nondeterministic changes in the system. This setting raises the questions of how to represent the plans and how to perform plan search. The answers are quite different from those in the simpler classical framework. In this paper, we approach conditional planning from a new viewpoint that is motivated by the use of satisfiability algorithms in classical planning. Translating conditional planning to formulae in the propositional logic is not feasible because of inherent computational limitations. Instead, we translate conditional planning to quantified Boolean formulae. We discuss three formalizations of conditional planning as quantified Boolean formulae, and pr...
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...e new techniques disabled cannot solve any of the benchmarks in Table 3 in less than 4 hours (14400 seconds.) The techniques for improving the obvious algorithm are based on failed literal detection (=-=Freeman, 1995-=-; Li & Anbulagan, 1997), and for formulae 9X8Y \Phi on performing computation with the universal variables Y before all variables in X have been assigned a truth-value. First, before performing exhaus...

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