Solving propositional satisfiability problems

Jeroslow, Robert G.; Wang, Jinchang

doi:10.1007/bf01531077

Cited by 164 publications

(91 citation statements)

References 8 publications

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“…The motivation behind this heuristic is that in a list of clauses with n variables, there are 2 n truth valuations and a clause of length p rules out exactly 2 n−p of these valuations. Using the above motivation, JeroslowWang justify their rule as one that tends to branch to a sub-problem that is most likely to be satisfiable ( [5], pp. 172-173).…”

Section: Literal Activity and Clause Lengthmentioning

confidence: 99%

“…Early branching heuristics, such as Bohm's heuristic [3], Maximum Occurrences on Minimum sized clauses (MOM) [4] and Jeroslow-Wang heuristic [5], attempt to resolve smaller clauses first as that might result in earlier conflicts and implications. However, these heuristics are unable to solve large (industrial) problems that one encounters in contemporary EDA problem formulations.…”

Section: Introductionmentioning

confidence: 99%

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Guiding CNF-SAT Search by Analyzing Constraint-Variable Dependencies and Clause Lengths

Durairaj

Kalla

2006

2006 IEEE International High Level Design Validation and Test Workshop

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The type of decision strategies employed for CNF-SAT have a profound effect on the efficiency and performance of SAT engines. Over the years, a variety of decision heuristics have been proposed; each has its own achievements and limitations. This paper re-visits the issue of decision heuristics and engineers a new approach that takes an integrated view of the overall problem structure. Our approach qualitatively analyzes clause-variable dependencies by accounting for variable/literal activity, clause connectivity, distribution of variables among clauses of different lengths, and correlation among variables, to derive an initial static ordering for SAT search. To account for conflict clauses and their resolution, a corresponding dynamic variable order update strategy is also presented. Quantitative metrics are proposed that are used to devise an algorithmic approach to guide overall SAT search. Experimental results demonstrate that our strategy significantly outperforms conventional approaches.

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Section: Literal Activity and Clause Lengthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Guiding CNF-SAT Search by Analyzing Constraint-Variable Dependencies and Clause Lengths

Durairaj

Kalla

2006

2006 IEEE International High Level Design Validation and Test Workshop

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“…Such a lower bound was considered in [15]. -Jeroslow-Wang (JW) [7]: given a formula φ, for each literal L of φ the following function is defined: J(L) = L∈C∈φ 2 −|C| , where |C| is the length of clause C. JW selects a variable p of φ among those that maximize J(p)+J(¬p).…”

Section: Branch and Bound For Max-satmentioning

confidence: 99%

A Max-SAT Solver with Lazy Data Structures

Alsinet

Manyà

Planes

2004

Advances in Artificial Intelligence – IBERAMIA 2004

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“…Jeroslow a n d W ang justify their rule as one that tends to branch to a subproblem that is most likely to be satis able ( 17], pp. 172-173).…”

Section: The Satisfaction Hypothesismentioning

confidence: 99%

Branching rules for satisfiability

Hooker

Vinay

1994

Lecture Notes in Computer Science

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Recent experience suggests that branching algorithms are among the most attractive for solving propositional satis ability problems. A k ey factor in their success is the rule they use to decide on which v ariable to branch next. We attempt to explain and improve the performance of branching rules with an empirical model-building approach. One model is based on the rationale given for the Jeroslow-Wang rule, variations of which have performed well in recent w ork. The model is refuted by carefully designed computational experiments. A second model explains the success of the Jeroslow-Wang rule, makes other predictions con rmed by experiment, and leads to the design of branching rules that are clearly superior to Jeroslow-Wang.Recent computational studies 2, 7, 13, 21] suggest that branching algorithms are among the most attractive for solving the propositional satis ability problem. An important factor in their success|perhaps the dominant factor|is the branching rule they use 13]. This is a rule that decides, at each node of an enumeration tree, which variables should be set to true or false in order to generate the children of that node. A clever branching rule can reduce the size of the search tree by several orders of magnitude.One rule that has been found to be particularly e ective in a wide variety o f problems 13] is the Jeroslow-Wang rule 17], which w e de ne below. Another promising rule is the shortest positive clause rule used by Gallo and Urbani in their Horn relaxation algorithm 11]. There is little understanding, however, of when and why these rules work well.Our purpose here is to try to improve our understanding of branching rules and to design better ones. We will show that the original motivation for the J-W rule, namely that it takes a branch in which one is most likely to nd a satisfying truth assignment, does not explain its performance. A proper explanation is considerably more nuanced and reveals that the original motivation produces a good rule only through a remarkable coincidence.GSIA Working Paper 1994-09. The rst author is partially supported by ONR grant N00014-92-J-1028. The authors wish to thank Ajai Kapoor for assistance in computational testing and statistical analysis.

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Solving propositional satisfiability problems

Cited by 164 publications

References 8 publications

Guiding CNF-SAT Search by Analyzing Constraint-Variable Dependencies and Clause Lengths

Guiding CNF-SAT Search by Analyzing Constraint-Variable Dependencies and Clause Lengths

A Max-SAT Solver with Lazy Data Structures

Branching rules for satisfiability

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