Effective Preprocessing in SAT Through Variable and Clause Elimination

Eén, Niklas; Biere, Armin

doi:10.1007/11499107_5

Cited by 427 publications

(396 citation statements)

References 20 publications

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“…The tradeoff is regulated by the choice of the techniques applied to infer binary clauses, considering the power and cost. See for example [7] and the references therein.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

“…In contrast, the CNF representing the allDiff constraint with the initial equations E 1 consists of 76 clauses with 23 variables and after applying SatELite [7] this is reduced to 57 clauses with 16 variables. Examining this reduced CNF reveals that it contains binary clauses corresponding to the equations in E 2 but not those from E 3 .…”

Section: Related Work and Conclusionmentioning

confidence: 99%

See 1 more Smart Citation

Boolean Equi-propagation for Optimized SAT Encoding

Metodi

Codish

Lagoon

et al. 2011

Principles and Practice of Constraint Programming – CP 2011

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Abstract. We present an approach to propagation based solving, Boolean equi-propagation, where constraints are modelled as propagators of information about equalities between Boolean literals. Propagation based solving applies this information as a form of partial evaluation resulting in optimized SAT encodings. We demonstrate for a variety of benchmarks that our approach results in smaller CNF encodings and leads to speed-ups in solving times.

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“…The tradeoff is regulated by the choice of the techniques applied to infer binary clauses, considering the power and cost. See for example [7] and the references therein.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Section: Related Work and Conclusionmentioning

confidence: 99%

Boolean Equi-propagation for Optimized SAT Encoding

Metodi

Codish

Lagoon

et al. 2011

Principles and Practice of Constraint Programming – CP 2011

View full text Add to dashboard Cite

show abstract

“…This suggests the use of a generalpurpose SAT solver to solve the constraint satisfaction problem. We performed an experiment using MiniSat version 2.0 beta [10,9], which is one of the best publicly available SAT solvers. We always use the degree-five predicate P 5 (x) = x 1 ⊕ x 2 ⊕ x 3 ⊕ (x 4 ∧ x 5 ).…”

Section: A Minisat Experimentsmentioning

confidence: 99%

Goldreich’s One-Way Function Candidate and Myopic Backtracking Algorithms

Cook

Etesami

Miller

et al. 2009

Lecture Notes in Computer Science

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Abstract. Goldreich (ECCC 2000) proposed a candidate one-way function construction which is parameterized by the choice of a small predicate (over d = O(1) variables) and of a bipartite expanding graph of right-degree d. The function is computed by labeling the n vertices on the left with the bits of the input, labeling each of the n vertices on the right with the value of the predicate applied to the neighbors, and outputting the n-bit string of labels of the vertices on the right.Inverting Goldreich's one-way function is equivalent to finding solutions to a certain constraint satisfaction problem (which easily reduces to SAT) having a "planted solution," and so the use of SAT solvers constitutes a natural class of attacks.We perform an experimental analysis using MiniSat, which is one of the best publicly available algorithms for SAT. Our experiment shows that the running time required to invert the function grows exponentially with the length of the input, and that such an attack becomes infeasible already with small input length (a few hundred bits).Motivated by these encouraging experiments, we initiate a rigorous study of the limitations of back-tracking based SAT solvers as attacks against Goldreich's function. Results by Alekhnovich, Hirsch and Itsykson imply that Goldreich's function is secure against "myopic" backtracking algorithms (an interesting subclass) if the 3-ary parity predicate P (x1, x2, x3) = x1 ⊕ x2 ⊕ x3 is used. One must, however, use non-linear predicates in the construction, which otherwise succumbs to a trivial attack via Gaussian elimination.We generalized the work of Alekhnovich et al. to handle a more general class of predicates, and we present a lower bound for the construction that uses the predicate P d (x1, . . . , x d ) := x1 ⊕x2 ⊕· · ·⊕x d−2 ⊕(x d−1 ∧x d ) and a random graph.

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“…Of course, with respect to full first-order logic, these methods are inherently incomplete. Further relevant techniques stem from knowledge compilation [34] and SAT solving, where Boolean variable elimination is an important preprocessing technique [6,27].…”

Section: Resultsmentioning

confidence: 99%

Abduction in Logic Programming as Second-Order Quantifier Elimination

Wernhard

2013

Frontiers of Combining Systems

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Abstract. It is known that skeptical abductive explanations with respect to classical logic can be characterized semantically in a natural way as formulas with second-order quantifiers. Computing explanations is then just elimination of the second-order quantifiers. By using application patterns and generalizations of second-order quantification, like literal projection, the globally weakest sufficient condition and circumscription, we transfer these principles in a unifying framework to abduction with three non-classical semantics of logic programming: stable model, partial stable model and well-founded semantics. New insights are revealed about abduction with the partial stable model semantics.

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Effective Preprocessing in SAT Through Variable and Clause Elimination

Cited by 427 publications

References 20 publications

Boolean Equi-propagation for Optimized SAT Encoding

Boolean Equi-propagation for Optimized SAT Encoding

Goldreich’s One-Way Function Candidate and Myopic Backtracking Algorithms

Abduction in Logic Programming as Second-Order Quantifier Elimination

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