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Black-Box Optimization in an Extended Search Space for SAT Solving

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11548))

Abstract

The Divide-and-Conquer approach is often used to solve hard instances of the Boolean satisfiability problem (SAT). In particular, it implies splitting an original SAT instance into a series of simpler subproblems. If this split satisfies certain conditions, then it is possible to use a stochastic pseudo-Boolean black-box function to estimate the time required for solving an original SAT instance with the chosen decomposition. One can use black-box optimization methods to minimize the function over the space of all possible decompositions. In the present study, we make use of peculiar features which stem from the NP-completeness of the Boolean satisfiability problem to improve this general approach. In particular, we show that the search space over which the black-box function is minimized can be extended by adding solver parameters and the SAT encoding parameters into it. In the computational experiments, we use the SMAC algorithm to optimize such black-box functions for hard SAT instances encoding the problems of cryptanalysis of several stream ciphers. The results show that the proposed approach outperforms the competition.

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Acknowledgements

Authors thank Dr. Alexander Semenov for valuable preliminary discussions regarding the SAT algorithms parameter tuning in the context of Divide-and-Conquer solving. We would also like to thank anonymous reviewers for their valuable comments that made it possible to improve the quality of the present paper. The research was partially supported by Council for Grants of the President of the Russian Federation (grant no. MK-4155.2018.9) and by Russian Foundation for Basic Research (grant no. 19-07-00746-a).

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  1. ISDCT SB RAS, Irkutsk, Russia

    Oleg Zaikin & Stepan Kochemazov

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  1. Oleg Zaikin
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  2. Stepan Kochemazov
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Correspondence to Oleg Zaikin .

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  1. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Yury Kochetov

  3. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Zaikin, O., Kochemazov, S. (2019). Black-Box Optimization in an Extended Search Space for SAT Solving. In: Khachay, M., Kochetov, Y., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Lecture Notes in Computer Science(), vol 11548. Springer, Cham. https://doi.org/10.1007/978-3-030-22629-9_28

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  • DOI: https://doi.org/10.1007/978-3-030-22629-9_28

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