Article

Effective preprocessing in SAT through variable and clause elimination

Authors:

Armin BiereAuthors Info & Claims

SAT'05: Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing

Pages 61 - 75

https://doi.org/10.1007/11499107_5

Published: 19 June 2005 Publication History

Abstract

Preprocessing SAT instances can reduce their size considerably. We combine variable elimination with subsumption and self-subsuming resolution, and show that these techniques not only shrink the formula further than previous preprocessing efforts based on variable elimination, but also decrease runtime of SAT solvers substantially for typical industrial SAT problems. We discuss critical implementation details that make the reduction procedure fast enough to be practical.

References

[1]

Subbarayan, S., Pradhan, D.: NiVER: Non increasing variable elimination resolution for preprocessing SAT instances. (In: Prel. Proc. SAT'04).

Digital Library

[2]

Davis, M., Logemann, G., Loveland, D.: A machine program for theorem proving. Comm. of the ACM 5 (1962).

Digital Library

[3]

Bacchus, F., Winter, J.: Effective preprocessing with hyper-resolution and equality reduction. In: Proc. SAT'03. (Volume 2919 of LNCS.).

[4]

Brafman, R.: A simplifier for propositional formulas with many binary clauses. IEEE Trans. on Systems, Man, and Cybernetics 34 (2004).

Digital Library

[5]

Lynce, I., Marques-Silva, J.: Probing-based preprocessing techniques for propositional satisfiability. (In: Proc. ICTAI'03).

Digital Library

[6]

Novikov, Y.: Local search for boolean relations on the basis of unit propagation. (In: Proc. of DATE'03).

Digital Library

[7]

Stålmarck, G.: A system for determining propositional logic theorems by applying values and rules to triplets that are generated from a formula (1989) Swedish Patent No 467 076.

[8]

Kunz, W., Pradhan, D.: Recursive learning: An attractive alternative to the decision tree for test generation in digital circuits. (In: Proc. ITC'92).

Digital Library

[9]

Kühlmann, A., Paruthi, V., Krohm, F., Ganai, M.: Robust boolean reasoning for equivalence checking and functional property verification. IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems 21 (2002).

Digital Library

[10]

Davis, M., Putnam, H.: A computing procedure for quantification theory. Journal of the ACM 7 (1960).

Digital Library

[11]

Chatalic, P., Simon, L.: ZRes: The old Davis-Putnam procedure meets ZBDDs. In: Proc. CADE'00. (Number 1831 in LNAI).

Digital Library

[12]

Biere, A.: Resolve and expand. (In: Prel. Proc. SAT'04).

Digital Library

[13]

Boy de la Tour, T.: An optimality result for clause form translation. Journal of Symbolic Computation 14 (1992).

Digital Library

[14]

Jackson, P., Sheridan, D.: Clause form conversions for boolean circuits. (In: Prel. Proc. SAT'04).

Digital Library

[15]

Plaisted, D., Greenbaum, S.: A structure-preserving clause form translation. Journal of Symbolic Computation 2 (1986).

Digital Library

[16]

Velev, M.: Efficient translation of boolean formulas to CNF in in formal verification of microprocessors. (In: Proc. ASP-DAC'04).

Digital Library

[17]

Tseitin, G.: On the complexity of derivation in propositional calculus. Studies in Constr. Math. and Math. Logic (1968).

[18]

Giunchiglia, E., Maratea, M., Tacchella, A.: Dependent and independent variables for propositional satisfiability. In: Proc. JELIA'02. (Volume 2424 of LNCS.).

Digital Library

[19]

Ostrowski, R., Grégoire, É., Mazure, B., Saïs, L.: Recovering and exploiting structural knowledge from CNF formulas. In: Proc. CP'02. (Volume 2470 of LNCS.).

Digital Library

[20]

Grégoire, É., Ostrowski, R., Mazure, B., Saïs, L.: Automatic extraction of functional dependencies. (In: Prel. Proc. SAT'04).

[21]

Eén, N., Sörensson, N.: An extensible SAT solver. In: Proc. SAT'03. (Volume 2919 of LNCS.).

[22]

Sörensson, N.: (Conflict clause simplification using subsumption resolution) paper in preparation.

[23]

Eén, N., Sörensson, N.: Temporal induction by incremental SAT solving. In: Proc. BMC'03. (Volume 89(4) of ENTCS.).

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Published In

cover image Guide Proceedings

SAT'05: Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing

June 2005

491 pages

ISBN:3540262768

Editors:
Fahiem Bacchus
Department of Computer Science, University of Toronto, Canada
,
Toby Walsh
Dept. of Computer Science, Trinity College, Dublin 2, Canada

Sponsors

INTEL: Intel Corporation
Cadence Design Systems
Microsoft Research: Microsoft Research
Intelligence Information Systems Institute: Intelligence Information Systems Institute
CoLogNet Network of Excellence: CoLogNet Network of Excellence

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 19 June 2005

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Cited By

Ibrahim AIbrahim AEl-Kharashi MSafar M(2024)Adaptive SAT Modeling for Optimal Pattern Retargeting in IEEE 1687 NetworksIEEE Transactions on Computers10.1109/TC.2023.333619873:2(536-547)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1109/TC.2023.3336198
Osama MWijs ABiere A(2024)Certified SAT solving with GPU accelerated inprocessingFormal Methods in System Design10.1007/s10703-023-00432-z62:1-3(79-118)Online publication date: 1-Jun-2024
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Francès de Mas J(2024)Binary Implication Hypergraphs for the Representation and Simplification of Propositional FormulaeLogic-Based Program Synthesis and Transformation10.1007/978-3-031-71294-4_4(64-81)Online publication date: 9-Sep-2024
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