Article

From sampling to model counting

Authors:

Carla P. Gomes,

Joerg Hoffmann,

Ashish Sabharwal,

Bart SelmanAuthors Info & Claims

IJCAI'07: Proceedings of the 20th international joint conference on Artifical intelligence

Pages 2293 - 2299

Published: 06 January 2007 Publication History

Abstract

We introduce a new technique for counting models of Boolean satisfiability problems. Our approach incorporates information obtained from sampling the solution space. Unlike previous approaches, our method does not require uniform or near-uniform samples. It instead converts local search sampling without any guarantees into very good bounds on the model count with guarantees. We give a formal analysis and provide experimental results showing the effectiveness of our approach.

References

[1]

{Bayardo Jr. and Pehoushek, 2000} R. J. Bayardo Jr. and J. D. Pehoushek. Counting models using connected components. In 17th AAAI, pg. 157-162, Austin, TX, Jul 2000.

Digital Library

[2]

{Darwiche, 2005} A. Darwiche. The quest for efficient probabilistic inference, Jul 2005. Invited Talk, IJCAI-05.

[3]

{Eén and Sörensson, 2005} N. Eén and N. Sörensson. MiniSat: A SAT solver with conflict-clause minimization. In 8th SAT, St. Andrews, U.K., Jun 2005. Poster.

[4]

{Gomes et al., 2006} C. P. Gomes, A. Sabharwal, and B. Selman. Model counting: A new strategy for obtaining good bounds. In 21th AAAI, pg. 54-61, Boston, MA, Jul 2006.

Digital Library

[5]

{Jerrum et al., 1986} M. R. Jerrum, L. G. Valiant, and V. V. Vazirani. Random generation of combinatorial structures from a uniform distribution. Theoretical Comput. Sci., 43:169-188, 1986.

Digital Library

[6]

{Kilby et al., 2006} P. Kilby, J. Slaney, S. Thiébaux, and T. Walsh. Estimating search tree size. In 21th AAAI, pg. 1014-1019, Boston, MA, Jul 2006.

Digital Library

[7]

{Kirkpatrick et al., 1983} S. Kirkpatrick, D. Gelatt Jr., and M. Vecchi. Optimization by simuleated annealing. Science, 220(4598):671-680, 1983.

[8]

{Littman et al., 2001} M. L. Littman, S.M.Majercik, and T. Pitassi. Stochastic Boolean satisfiability. J. Auto. Reas., 27(3):251-296, 2001.

Digital Library

[9]

{Madras, 2002} N. Madras. Lectures on Monte Carlo methods. In Field Institute Monographs, volume 16. Amer. Math. Soc., 2002.

[10]

{McAllester et al., 1997} D. A. McAllester, B. Selman, and H. Kautz. Evidence for invariants in local search. In AAAI/IAAI, pg. 321-326, Providence, RI, Jul 1997.

Digital Library

[11]

{Metropolis et al., 1953} N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller. Equations of state calculations by fast computing machines. J. Chem. Phy., 21:1087-1092, 1953.

[12]

{Park, 2002} J. D. Park. MAP complexity results and approximation methods. In 18th UAI, pg. 388-396, Edmonton, Canada, Aug 2002.

Digital Library

[13]

{Roth, 1996} D. Roth. On the hardness of approximate reasoning. J. AI, 82(1-2):273-302, 1996.

Digital Library

[14]

{Sang et al., 2004} T. Sang, F. Bacchus, P. Beame, H. A. Kautz, and T. Pitassi. Combining component caching and clause learning for effective model counting. In 7th SAT, Vancouver, B.C., Canada, May 2004. Online Proceedings.

[15]

{Sang et al., 2005} T. Sang, P. Beame, and H. A. Kautz. Performing Bayesian inference by weighted model counting. In 20th AAAI, pg. 475-482, Pittsburgh, PA, Jul 2005.

Digital Library

[16]

{Toda, 1989} S. Toda. On the computational power of PP and ⊕P. In 30th FOCS, pg. 514-519, 1989.

Digital Library

[17]

{Wei and Selman, 2005} W. Wei and B. Selman. A new approach to model counting. In 8th SAT, volume 3569 of LNCS, pg. 324-339, St. Andrews, U.K., Jun 2005.

Digital Library

[18]

{Wei et al., 2004} W. Wei, J. Erenrich, and B. Selman. Towards efficient sampling: Exploiting random walk strategies. In 19th AAAI, pg. 670-676, San Jose, CA, Jul 2004.

Digital Library

Cited By

Pavan AVinodchandran NBhattacharyya AMeel K(2022)Model Counting Meets Distinct Elements in a Data StreamACM SIGMOD Record10.1145/3542700.354272151:1(87-94)Online publication date: 1-Jun-2022
https://dl.acm.org/doi/10.1145/3542700.3542721
Bao QWang ZLi XLarus JWu D(2021)AbacusProceedings of the 43rd International Conference on Software Engineering10.1109/ICSE43902.2021.00078(797-809)Online publication date: 22-May-2021
https://dl.acm.org/doi/10.1109/ICSE43902.2021.00078
Lee NWang YJiang J(2017)Solving stochastic boolean satisfiability under random-exist quantificationProceedings of the 26th International Joint Conference on Artificial Intelligence10.5555/3171642.3171741(688-694)Online publication date: 19-Aug-2017
https://dl.acm.org/doi/10.5555/3171642.3171741
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Information & Contributors

Information

Published In

cover image Guide Proceedings

IJCAI'07: Proceedings of the 20th international joint conference on Artifical intelligence

January 2007

2953 pages

Editors:
Rajeev Sangal
International Institute of Information Technology, Hyderabad
,
Harish Mehta
Onward Technologies Limited
,
R. K. Bagga
International Institute of Information Technology, Hyderabad

Sponsors

The International Joint Conferences on Artificial Intelligence, Inc.

Publisher

Morgan Kaufmann Publishers Inc.

San Francisco, CA, United States

Publication History

Published: 06 January 2007

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Cited By

Pavan AVinodchandran NBhattacharyya AMeel K(2022)Model Counting Meets Distinct Elements in a Data StreamACM SIGMOD Record10.1145/3542700.354272151:1(87-94)Online publication date: 1-Jun-2022
https://dl.acm.org/doi/10.1145/3542700.3542721
Bao QWang ZLi XLarus JWu D(2021)AbacusProceedings of the 43rd International Conference on Software Engineering10.1109/ICSE43902.2021.00078(797-809)Online publication date: 22-May-2021
https://dl.acm.org/doi/10.1109/ICSE43902.2021.00078
Lee NWang YJiang J(2017)Solving stochastic boolean satisfiability under random-exist quantificationProceedings of the 26th International Joint Conference on Artificial Intelligence10.5555/3171642.3171741(688-694)Online publication date: 19-Aug-2017
https://dl.acm.org/doi/10.5555/3171642.3171741
Wang JYin MWu J(2017)Two approximate algorithms for model countingTheoretical Computer Science10.1016/j.tcs.2016.04.047657:PA(28-37)Online publication date: 2-Jan-2017
https://dl.acm.org/doi/10.1016/j.tcs.2016.04.047
Chistikov DDimitrova RMajumdar R(2017)Approximate counting in SMT and value estimation for probabilistic programsActa Informatica10.1007/s00236-017-0297-254:8(729-764)Online publication date: 1-Dec-2017
https://dl.acm.org/doi/10.1007/s00236-017-0297-2
Bart AKoriche FLagniez JMarquis P(2016)An improved CNF encoding scheme for probabilistic inferenceProceedings of the Twenty-second European Conference on Artificial Intelligence10.3233/978-1-61499-672-9-613(613-621)Online publication date: 29-Aug-2016
https://dl.acm.org/doi/10.3233/978-1-61499-672-9-613
Vaisman RBotev ZRidder A(2016)Sequential Monte Carlo for counting vertex covers in general graphsStatistics and Computing10.1007/s11222-015-9546-926:3(591-607)Online publication date: 1-May-2016
https://dl.acm.org/doi/10.1007/s11222-015-9546-9
Beame PVan den Broeck GGribkoff ESuciu DMilo TCalvanese D(2015)Symmetric Weighted First-Order Model CountingProceedings of the 34th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/2745754.2745760(313-328)Online publication date: 20-May-2015
https://dl.acm.org/doi/10.1145/2745754.2745760
Chistikov DDimitrova RMajumdar R(2015)Approximate Counting in SMT and Value Estimation for Probabilistic ProgramsProceedings of the 21st International Conference on Tools and Algorithms for the Construction and Analysis of Systems - Volume 903510.1007/978-3-662-46681-0_26(320-334)Online publication date: 11-Apr-2015
https://dl.acm.org/doi/10.1007/978-3-662-46681-0_26
Lee NJiang JChang Y(2014)Towards formal evaluation and verification of probabilistic designProceedings of the 2014 IEEE/ACM International Conference on Computer-Aided Design10.5555/2691365.2691433(340-347)Online publication date: 3-Nov-2014
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