Optimal base encodings for Pseudo-Boolean constraints

Michael Codish; Yoav Fekete; Carsten Fuhs; Peter Schneider-Kamp

doi:10.1007/978-3-642-19835-9_16

Optimal base encodings for Pseudo-Boolean constraints

Michael Codish, Yoav Fekete, Carsten Fuhs, Peter Schneider-Kamp

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

11 Scopus citations

Abstract

This paper formalizes the optimal base problem, presents an algorithm to solve it, and describes its application to the encoding of Pseudo-Boolean constraints to SAT. We demonstrate the impact of integrating our algorithm within the Pseudo-Boolean constraint solver MiniSat⁺. Experimentation indicates that our algorithm scales to bases involving numbers up to 1,000,000, improving on the restriction in MiniSat⁺ to prime numbers up to 17. We show that, while for many examples primes up to 17 do suffice, encoding with respect to optimal bases reduces the CNF sizes and improves the subsequent SAT solving time for many examples.

Original language	English
Title of host publication	Tools and Algorithms for the Construction and Analysis of Systems - 17th Int. Conf., TACAS 2011, Held as Part of the Joint European Conf. on Theory and Practice of Software, ETAPS 2011, Proceedings
Pages	189-204
Number of pages	16
DOIs	https://doi.org/10.1007/978-3-642-19835-9_16
State	Published - 4 Apr 2011
Event	17th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2011, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2011 - Saarbrucken, Germany Duration: 26 Mar 2011 → 3 Apr 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6605 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	17th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2011, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2011
Country/Territory	Germany
City	Saarbrucken
Period	26/03/11 → 3/04/11

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/978-3-642-19835-9_16

Cite this

Codish, M., Fekete, Y., Fuhs, C., & Schneider-Kamp, P. (2011). Optimal base encodings for Pseudo-Boolean constraints. In Tools and Algorithms for the Construction and Analysis of Systems - 17th Int. Conf., TACAS 2011, Held as Part of the Joint European Conf. on Theory and Practice of Software, ETAPS 2011, Proceedings (pp. 189-204). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6605 LNCS). https://doi.org/10.1007/978-3-642-19835-9_16

Codish, Michael ; Fekete, Yoav ; Fuhs, Carsten et al. / Optimal base encodings for Pseudo-Boolean constraints. Tools and Algorithms for the Construction and Analysis of Systems - 17th Int. Conf., TACAS 2011, Held as Part of the Joint European Conf. on Theory and Practice of Software, ETAPS 2011, Proceedings. 2011. pp. 189-204 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "This paper formalizes the optimal base problem, presents an algorithm to solve it, and describes its application to the encoding of Pseudo-Boolean constraints to SAT. We demonstrate the impact of integrating our algorithm within the Pseudo-Boolean constraint solver MiniSat+. Experimentation indicates that our algorithm scales to bases involving numbers up to 1,000,000, improving on the restriction in MiniSat+ to prime numbers up to 17. We show that, while for many examples primes up to 17 do suffice, encoding with respect to optimal bases reduces the CNF sizes and improves the subsequent SAT solving time for many examples.",

author = "Michael Codish and Yoav Fekete and Carsten Fuhs and Peter Schneider-Kamp",

note = "Funding Information: Supported by GIF grant 966-116.6 and the Danish Natural Science Research Council.; 17th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2011, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2011 ; Conference date: 26-03-2011 Through 03-04-2011",

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Codish, M, Fekete, Y, Fuhs, C & Schneider-Kamp, P 2011, Optimal base encodings for Pseudo-Boolean constraints. in Tools and Algorithms for the Construction and Analysis of Systems - 17th Int. Conf., TACAS 2011, Held as Part of the Joint European Conf. on Theory and Practice of Software, ETAPS 2011, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6605 LNCS, pp. 189-204, 17th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2011, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2011, Saarbrucken, Germany, 26/03/11. https://doi.org/10.1007/978-3-642-19835-9_16

Optimal base encodings for Pseudo-Boolean constraints. / Codish, Michael; Fekete, Yoav; Fuhs, Carsten et al.
Tools and Algorithms for the Construction and Analysis of Systems - 17th Int. Conf., TACAS 2011, Held as Part of the Joint European Conf. on Theory and Practice of Software, ETAPS 2011, Proceedings. 2011. p. 189-204 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6605 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - This paper formalizes the optimal base problem, presents an algorithm to solve it, and describes its application to the encoding of Pseudo-Boolean constraints to SAT. We demonstrate the impact of integrating our algorithm within the Pseudo-Boolean constraint solver MiniSat+. Experimentation indicates that our algorithm scales to bases involving numbers up to 1,000,000, improving on the restriction in MiniSat+ to prime numbers up to 17. We show that, while for many examples primes up to 17 do suffice, encoding with respect to optimal bases reduces the CNF sizes and improves the subsequent SAT solving time for many examples.

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Codish M, Fekete Y, Fuhs C, Schneider-Kamp P. Optimal base encodings for Pseudo-Boolean constraints. In Tools and Algorithms for the Construction and Analysis of Systems - 17th Int. Conf., TACAS 2011, Held as Part of the Joint European Conf. on Theory and Practice of Software, ETAPS 2011, Proceedings. 2011. p. 189-204. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-19835-9_16

Optimal base encodings for Pseudo-Boolean constraints

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