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International Workshop on Frontiers in Algorithmics

FAW 2015: Frontiers in Algorithmics pp 229–240Cite as

Approximate Model Counting via Extension Rule

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9130))

Abstract

Resolution principle is an important rule of inference in theorem proving. Model counting using extension rule is considered as a counterpart to resolution-based methods for model counting. Based on the exact method, this paper proposes two approximate model counting algorithms, and proves the time complexity of the algorithms. Experimental results show that they have good performance in the accuracy and efficiency.

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Notes

  1. 1.

    If \(\sigma \) is very small, then \(S_{accur}\approx S_{appr}\). Consequently, \(\sigma \approx \sigma '=\frac{|S_{accur}-S_{appr}|}{S_{appr}}\). So \(\sigma '\) is also considered as approximate dispersion. In this paper, we use \(\sigma '\) to get the approximate number of unsatisfying assignments of \(\varSigma \), because it is difficult to use \(\sigma \) in the condition that we do not know the exact number of unsatisfying assignments of \(\varSigma \). However, in the experimental results, we obtain the approximate value of models and know the exact number of models, so we use \(\sigma \) to measure the two approximate algorithms.

  2. 2.

    When \(sumterm\) is the value of the first sum term, \(svalue = 0\). In this case, we can not run the division operator, so we restrict \(i\ge 2\); because model counting is generally to count the number of models of a Boolean formula, the number of unsatisfying assignments is less than \(2^{v}\). So we restrict its approximate value is less than \(2^{v}\).

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Acknowledgments

This paper was supported by the National Key Basic Research Program of China (973 Program, No. 2012CB326403), National Natural Science Foundation of China (Nos. 61272535, 61370156, 61363035, 61165009), Guangxi “Bagui Scholar” Teams for Innovation and Research Project, Guangxi Natural Science Foundation (No. 2013GXNSFBA019263), Science and Technology Research Projects of Guangxi Higher Education (Nos. 2013YB028, 2013YB029), Scientific Research Foundation of Guangxi Normal University for Doctors, and Guangxi Collaborative Innovation Center of Multisource Information Integration and Intelligent Processing.

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Authors and Affiliations

  1. Guangxi Key Lab of Multi-source Information Mining & Security, Guangxi Normal University, Guilin, China

    Jinyan Wang & Jingli Wu

  2. College of Computer Science and Information Technology, Guangxi Normal University, Guilin, China

    Jinyan Wang & Jingli Wu

  3. School of Computer Science and Information Technology, Northeast Normal University, Changchun, China

    Minghao Yin

Authors
  1. Jinyan Wang
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  2. Minghao Yin
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  3. Jingli Wu
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Correspondence to Jinyan Wang .

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Editors and Affiliations

  1. Central South University, Changsha, China

    Jianxin Wang

  2. Courant Institute, New York University, New York, New York, USA

    Chee Yap

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Wang, J., Yin, M., Wu, J. (2015). Approximate Model Counting via Extension Rule. In: Wang, J., Yap, C. (eds) Frontiers in Algorithmics. FAW 2015. Lecture Notes in Computer Science(), vol 9130. Springer, Cham. https://doi.org/10.1007/978-3-319-19647-3_22

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  • DOI: https://doi.org/10.1007/978-3-319-19647-3_22

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