Abstract
In this paper we propose the approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. We suggest the approach based on the Monte Carlo method for estimating time of processing of an arbitrary partitioning. We solve the problem of search for a partitioning with good effectiveness via the optimization of the special predictive function over the finite search space. For this purpose we use the tabu search strategy. In our computational experiments we found partitionings for SAT instances encoding problems of inversion of some cryptographic functions. Several of these SAT instances with realistic predicted solving time were successfully solved on a computing cluster and in the volunteer computing project SAT@home. The solving time agrees well with estimations obtained by the proposed method.
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Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press, Amsterdam (2009)
Biryukov, A., Shamir, A., Wagner, D.: Real time cryptanalysis of A5/1 on a PC. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 1–18. Springer, Heidelberg (2001)
De Cannière, C.: Trivium: a stream cipher construction inspired by block cipher design principles. In: Katsikas, S.K., López, J., Backes, M., Gritzalis, S., Preneel, B. (eds.) ISC 2006. LNCS, vol. 4176, pp. 171–186. Springer, Heidelberg (2006)
Eibach, T., Pilz, E., Völkel, G.: Attacking bivium using SAT solvers. In: Kleine Büning, H., Zhao, X. (eds.) SAT 2008. LNCS, vol. 4996, pp. 63–76. Springer, Heidelberg (2008)
Glover, F., Laguna, M.: Tabu Search. Kluwer Academic Publishers, NewYork (1997)
Hyvärinen, A.E.J.: Grid Based Propositional Satisfiability Solving. Ph.d. thesis, Aalto University (2011)
Marques-Silva, J., Lynce, I., Malik, S.: Conflict-driven clause learning SAT solvers. In: Biere et al. [1], pp. 131–153
Metropolis, N., Ulam, S.: The monte carlo method. J. Amer. statistical assoc. 44(247), 335–341 (1949)
Otpuschennikov, I., Semenov, A., Kochemazov, S.: Transalg: a tool for translating procedural descriptions of discrete functions to SAT (tool paper). CoRR abs/1405.1544 (2014)
Semenov, A., Zaikin, O., Bespalov, D., Posypkin, M.: Parallel logical cryptanalysis of the generator A5/1 in BNB-grid system. In: Malyshkin, V. (ed.) PaCT 2011. LNCS, vol. 6873, pp. 473–483. Springer, Heidelberg (2011)
Soos, M., Nohl, K., Castelluccia, C.: Extending SAT solvers to cryptographic problems. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 244–257. Springer, Heidelberg (2009)
Acknowledgements
The authors wish to thank Stepan Kochemazov for numerous valuable comments. This work was partly supported by Russian Foundation for Basic Research (grants 14-07-00403-a and 15-07-07891-a) and by the President of Russian Federation grant for young scientists SP-1184.2015.5.
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Semenov, A., Zaikin, O. (2015). Using Monte Carlo Method for Searching Partitionings of Hard Variants of Boolean Satisfiability Problem. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2015. Lecture Notes in Computer Science(), vol 9251. Springer, Cham. https://doi.org/10.1007/978-3-319-21909-7_21
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DOI: https://doi.org/10.1007/978-3-319-21909-7_21
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