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Finding Effective SAT Partitionings Via Black-Box Optimization

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Black Box Optimization, Machine Learning, and No-Free Lunch Theorems

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 170))

Abstract

In the present chapter we study one method for partitioning hard instances of the Boolean satisfiability problem (SAT). It uses a subset of a set of variables of an original formula to partition it into a family of subproblems that are significantly easier to solve individually. While it is usually very hard to estimate the time required to solve a hard SAT instance without actually solving it, the partitionings of the presented kind make it possible to naturally construct such estimations via the well-known Monte Carlo method. We show that the problem of finding a SAT partitioning with minimal estimation of time required to solve all subproblems can be formulated as the problem of minimizing a special pseudo-Boolean black-box function. The experimental part of the paper clearly shows that in the context of the proposed approach relatively simple black-box optimization algorithms show good results in application to minimization of the functions of the described kind even when faced with hard SAT instances that encode problems of finding preimages of cryptographic functions.

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Notes

  1. 1.

    https://github.com/Nauchnik/pdsat.

  2. 2.

    https://github.com/Nauchnik/alias.

  3. 3.

    https://github.com/lytr777/CryptoEv.

  4. 4.

    Irkutsk Supercomputer Center of SB RAS, http://hpc.icc.ru.

References

  1. Audet, C., Hare, W.: Derivative-Free and Blackbox Optimization. Springer Series in Operations Research and Financial Engineering, Springer, Berlin (2017). https://doi.org/10.1007/978-3-319-68913-5

  2. Babenko, L.K., Maro, E.A., Anikeev, M.V.: Application of algebraic cryptanalysis to MAGMA and PRESENT block encryption standards. In: Proceedings of IEEE 11th International Conference on Application of Information and Communication Technologies (AICT), pp. 1–7 (2017). https://doi.org/10.1109/ICAICT.2017.8686954

  3. Balyo, T., Sinz, C.: Parallel satisfiability. In: Hamadi, Y., Sais, L. (eds.) Handbook of Parallel Constraint Reasoning, pp. 3–29. Springer, Berlin (2018). https://doi.org/10.1007/978-3-319-63516-3_1

    Chapter  Google Scholar 

  4. Bard, G.V.: Algebraic Cryptanalysis, 1st edn. Springer, Berlin (2009)

    Book  MATH  Google Scholar 

  5. Bessiere, C., Katsirelos, G., Narodytska, N., Walsh, T.: Circuit complexity and decompositions of global constraints. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence - IJCAI’09, pp. 412–418 (2009)

    Google Scholar 

  6. 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)

    Google Scholar 

  7. Biryukov, A., Shamir, A., Wagner, D.A.: Real time cryptanalysis of A5/1 on a PC. In: Schneier, B. (ed.) Fast Software Encryption, 7th International Workshop, FSE 2000. Lecture Notes in Computer Science, vol. 1978, pp. 1–18. Springer, Berlin (2000). https://doi.org/10.1007/3-540-44706-7_1

    Google Scholar 

  8. Boros, E., Hammer, P.L.: Pseudo-Boolean optimization. Discrete Appl. Math. 123(1–3), 155–225 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bouillaguet, C., Derbez, P., Fouque, P.: Automatic search of attacks on round-reduced AES and applications. In: Rogaway, P. (ed.) Advances in Cryptology - CRYPTO 2011 - 31st Annual Cryptology Conference. Lecture Notes in Computer Science, vol. 6841, pp. 169–187. Springer, Berlin (2011). https://doi.org/10.1007/978-3-642-22792-9_10

    Chapter  Google Scholar 

  10. Cannière, C.D., Preneel, B.: Trivium. In: Robshaw, M.J.B., Billet, O. (eds.) New Stream Cipher Designs - The eSTREAM Finalists. Lecture Notes in Computer Science, vol. 4986, pp. 244–266. Springer, Berlin (2008)

    Chapter  Google Scholar 

  11. Carter, K., Foltzer, A., Hendrix, J., Huffman, B., Tomb, A.: SAW: the software analysis workbench. In: Boleng, J., Taft, S.T. (eds.) Proceedings of the 2013 ACM SIGAda Annual Conference on High Integrity Language Technology, HILT, pp. 15–18. ACM, New York (2013). https://doi.org/10.1145/2527269.2527277

    Chapter  Google Scholar 

  12. Chang, C.L., Lee, R.C.T.: Symbolic Logic and Mechanical Theorem Proving, 1st edn. Academic Press, Cambridge (1997)

    MATH  Google Scholar 

  13. Clarke, E.M., Kroening, D., Lerda, F.: A tool for checking ANSI-C programs. In: Jensen, K., Podelski, A. (eds.) Tools and Algorithms for the Construction and Analysis of Systems, 10th International Conference, TACAS 2004. Lecture Notes in Computer Science, vol. 2988, pp. 168–176. Springer, Berlin (2004). https://doi.org/10.1007/978-3-540-24730-2_15

    Google Scholar 

  14. Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of the 3rd Annual ACM Symposium on Theory of Computing, pp. 151–158 (1971)

    Google Scholar 

  15. Cook, S.A., Mitchell, D.G.: Finding hard instances of the satisfiability problem: a survey. In: Satisfiability Problem: Theory and Applications. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 35, pp. 1–18. American Mathematical Society, Providence (1996)

    Google Scholar 

  16. Courtois, N.T.: Algebraic complexity reduction and cryptanalysis of GOST. IACR Cryptol. ePrint Arch. 2011, 626 (2011). http://eprint.iacr.org/2011/626

  17. Courtois, N.T., Gawinecki, J.A., Song, G.: Contradiction immunity and guess-then-determine attacks on GOST. Tatra Mt. Math. Publ. 53(1), 2–13 (2012)

    MathSciNet  MATH  Google Scholar 

  18. Daemen, J., Rijmen, V.: The Design of Rijndael: AES - The Advanced Encryption Standard. Information Security and Cryptography. Springer, Berlin (2002). https://doi.org/10.1007/978-3-662-04722-4

  19. Dowling, W.F., Gallier, J.H.: Linear-time algorithms for testing the satisfiability of propositional horn formulae. J. Log. Program. 1(3), 267–284 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  20. Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) Theory and Applications of Satisfiability Testing, 6th International Conference, SAT 2003. Selected Revised Papers. Lecture Notes in Computer Science, vol. 2919, pp. 502–518. Springer, Berlin (2003). https://doi.org/10.1007/978-3-540-24605-3_37

    MATH  Google Scholar 

  21. Eén, N., Sörensson, N.: Temporal induction by incremental SAT solving. Electr. Notes Theor. Comput. Sci. 89(4), 543–560 (2003)

    Article  MATH  Google Scholar 

  22. Eibach, T., Pilz, E., Völkel, G.: Attacking Bivium using SAT solvers. In: Büning, H.K., Zhao, X. (eds.) Theory and Applications of Satisfiability Testing - SAT 2008, 11th International Conference, SAT 2008. Lecture Notes in Computer Science, vol. 4996, pp. 63–76. Springer, Berlin (2008). https://doi.org/10.1007/978-3-540-79719-7_7

    MATH  Google Scholar 

  23. Feller, W.: An Introduction to Probability Theory and Its Applications, Volume II. Wiley, New York (1971)

    Google Scholar 

  24. Franco, J., Martin, J.: A history of satisfiability. In: Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 3–74. IOS Press, Amsterdam (2009)

    Google Scholar 

  25. Garey, M.R., Johnson, D.S.: Computers and Intractability, vol. 174. Freeman, New York (1979)

    MATH  Google Scholar 

  26. Glover, F.: Future paths for integer programming and links to artificial intelligence. Comput. OR 13(5), 533–549 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  27. Gomes, C.P., Sabharwal, A.: Exploiting runtime variation in complete solvers. In: Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 271–288. IOS Press, Amsterdam (2009)

    Google Scholar 

  28. Günther, C.G.: Alternating step generators controlled by de Bruijn sequences. In: Chaum, D., Price, W.L. (eds.) Advances in Cryptology - EUROCRYPT’87, Workshop on the Theory and Application of Cryptographic Techniques. Lecture Notes in Computer Science, vol. 304, pp. 5–14. Springer, Berlin (1987). https://doi.org/10.1007/3-540-39118-5_2

    Google Scholar 

  29. Hamadi, Y., Jabbour, S., Sais, L.: Manysat: a parallel SAT solver. J. Satisf. Boolean Model. Comput. 6(4), 245–262 (2009)

    MATH  Google Scholar 

  30. Hamming, R.W.: Error detecting and error correcting codes. Bell Syst. Tech. J. 29(2), 147–160 (1950). https://doi.org/10.1002/j.1538-7305.1950.tb00463.x

    Article  MathSciNet  MATH  Google Scholar 

  31. Hell, M., Johansson, T., Maximov, A., Meier, W.: The Grain family of stream ciphers. In: Robshaw, M.J.B., Billet, O. (eds.) New Stream Cipher Designs - The eSTREAM Finalists. Lecture Notes in Computer Science, vol. 4986, pp. 179–190. Springer, Berlin (2008)

    Chapter  Google Scholar 

  32. Heule, M., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: guiding CDCL SAT solvers by lookaheads. In: Eder, K., Lourenço, J., Shehory, O. (eds.) Hardware and Software: Verification and Testing - 7th International Haifa Verification Conference, HVC 2011. Lecture Notes in Computer Science, vol. 7261, pp. 50–65. Springer, Berlin (2011). https://doi.org/10.1007/978-3-642-34188-5_8

    Google Scholar 

  33. Heule, M.J.H., Kullmann, O., Marek, V.W.: Solving and verifying the Boolean Pythagorean triples problem via cube-and-conquer. In: Creignou, N., Le Berre, D. (eds.) Theory and Applications of Satisfiability Testing – SAT 2016. Lecture Notes in Computer Science, vol. 9710, pp. 228–245. Springer, Berlin (2016)

    Chapter  Google Scholar 

  34. Hyvärinen, A.E.J.: Grid based propositional satisfiability solving. Ph.D. Thesis, Aalto University (2011)

    Google Scholar 

  35. Hyvärinen, A.E.J., Junttila, T.A., Niemelä, I.: Partitioning SAT instances for distributed solving. In: Fermüller, C.G., Voronkov, A. (eds.) Logic for Programming, Artificial Intelligence, and Reasoning, LPAR-17, pp. 372–386. Springer, Berlin (2010). https://doi.org/10.1007/978-3-642-16242-8_27

    Chapter  MATH  Google Scholar 

  36. Janicic, P.: URSA: a system for uniform reduction to SAT. Log. Meth. Comput. Sci. 8(3), 1–39 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  37. Järvisalo, M., Junttila, T.: Limitations of restricted branching in clause learning. Constraints 14(3), 325–356 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  38. Järvisalo, M., Biere, A., Heule, M.: Simulating circuit-level simplifications on CNF. J. Autom. Reason. 49(4), 583–619 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  39. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  40. Kochemazov, S., Zaikin, O.: ALIAS: a modular tool for finding backdoors for SAT. In: Beyersdorff, O., Wintersteiger, C.M. (eds.) Theory and Applications of Satisfiability Testing - 21st International Conference, SAT 2018. Lecture Notes in Computer Science, vol. 10929, pp. 419–427. Springer, Berlin (2018). https://doi.org/10.1007/978-3-319-94144-8_25

    Chapter  MATH  Google Scholar 

  41. Kolda, T.G., Lewis, R.M., Torczon, V.: Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev. 45(3), 385–482 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  42. Kroening, D.: Software verification. In: Biere et al. [6], pp. 505–532

    Google Scholar 

  43. Lafitte, F.: Cryptosat: a tool for SAT-based cryptanalysis. IET Inf. Secur. 12(6), 463–474 (2018). https://doi.org/10.1049/iet-ifs.2017.0176

    Article  Google Scholar 

  44. Levin, L.: Universal sequential search problems. Probl. Inf. Transm. 9, 265–266 (1973)

    Google Scholar 

  45. Luke, S.: Essentials of Metaheuristics, 2nd edn. Lulu, Morrisville (2013). http://cs.gmu.edu/~sean/book/metaheuristics/

  46. Marques-Silva, J.P., Sakallah, K.A.: GRASP - a new search algorithm for satisfiability. In: Rutenbar, R.A., Otten, R.H.J.M. (eds.) Proceedings of the 1996 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 1996, pp. 220–227. IEEE Computer Society/ACM, New York (1996). https://doi.org/10.1109/ICCAD.1996.569607

    Google Scholar 

  47. Marques-Silva, J.P., Lynce, I., Malik, S.: Conflict-driven clause learning SAT solvers. In: Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 131–153. IOS Press, Amsterdam (2009)

    Google Scholar 

  48. Maximov, A., Biryukov, A.: Two trivial attacks on trivium. In: Adams, C.M., Miri, A., Wiener, M.J. (eds.) Selected Areas in Cryptography, 14th International Workshop, SAC 2007, Revised Selected Papers. Lecture Notes in Computer Science, vol. 4876, pp. 36–55. Springer, Berlin (2007). https://doi.org/10.1007/978-3-540-77360-3_3

    Google Scholar 

  49. Mcdonald, C., Charnes, C., Pieprzyk, J.: Attacking Bivium with MiniSat. Tech. Rep. 2007/040, ECRYPT Stream Cipher Project (2007)

    Google Scholar 

  50. Menezes, A.J., Vanstone, S.A., Oorschot, P.C.V.: Handbook of Applied Cryptography, 1st edn. CRC Press, Boca Raton (1996)

    MATH  Google Scholar 

  51. Metropolis, N., Ulam, S.: The Monte Carlo Method. J. Am. Stat. Assoc. 44(247), 335–341 (1949)

    Article  MATH  Google Scholar 

  52. Mühlenbein, H.: How genetic algorithms really work: mutation and hillclimbing. In: Männer, R., Manderick, B. (eds.) Parallel Problem Solving from Nature 2, PPSN-II, pp. 15–26. Elsevier, Amsterdam (1992)

    Google Scholar 

  53. Otpuschennikov, I.V., Semenov, A.A., Gribanova, I., Zaikin, O., Kochemazov, S.: Encoding cryptographic functions to SAT using TRANSALG system. In: Kaminka, G.A., Fox, M., Bouquet, P., Hüllermeier, E., Dignum, V., Dignum, F., van Harmelen, F. (eds.) ECAI 2016 - 22nd European Conference on Artificial Intelligence. Frontiers in Artificial Intelligence and Applications, vol. 285, pp. 1594–1595. IOS Press, Amsterdam (2016). https://doi.org/10.3233/978-1-61499-672-9-1594

    Google Scholar 

  54. Pavlenko, A., Buzdalov, M., Ulyantsev, V.: Fitness comparison by statistical testing in construction of SAT-based guess-and-determine cryptographic attacks. In: Auger, A., Stützle, T. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2019, pp. 312–320 (2019). https://doi.org/10.1145/3321707.3321847

    Google Scholar 

  55. Pavlenko, A., Semenov, A.A., Ulyantsev, V.: Evolutionary computation techniques for constructing SAT-based attacks in algebraic cryptanalysis. In: Kaufmann, P., Castillo, P.A. (eds.) Applications of Evolutionary Computation - 22nd International Conference, EvoApplications 2019. Lecture Notes in Computer Science, vol. 11454, pp. 237–253. Springer, Berlin (2019). https://doi.org/10.1007/978-3-030-16692-2_16

    Google Scholar 

  56. Posypkin, M., Semenov, A.A., Zaikin, O.: Using BOINC desktop grid to solve large scale SAT problems. Comput. Sci. (AGH) 13(1), 25–34 (2012)

    Google Scholar 

  57. Rios, L., Sahinidis, N.: Derivative-free optimization: a review of algorithms and comparison of software implementations. J. Global Optim. 56, 1247–1293 (2013). https://doi.org/10.1007/s10898-012-9951-y

    Article  MathSciNet  MATH  Google Scholar 

  58. Robinson, J.A.: A machine-oriented logic based on the resolution principle. J. ACM 12(1), 23–41 (1965). https://doi.org/10.1145/321250.321253

    Article  MathSciNet  MATH  Google Scholar 

  59. Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach, 3rd edn. Prentice Hall, Upper Saddle River (2009)

    Google Scholar 

  60. Semenov, A.: Decomposition representations of logical equations in problems of inversion of discrete functions. J. Comput. Syst. Sci. Int. 48, 718–731 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  61. Semenov, A.A., Zaikin, O.: Using Monte Carlo method for searching partitionings of hard variants of Boolean satisfiability problem. In: Malyshkin, V. (ed.) Parallel Computing Technologies - 13th International Conference, PaCT 2015. Lecture Notes in Computer Science, vol. 9251, pp. 222–230. Springer, Berlin (2015). https://doi.org/10.1007/978-3-319-21909-7_21

    Google Scholar 

  62. Semenov, A.A., Zaikin, O.: On the accuracy of statistical estimations of SAT partitionings effectiveness in application to discrete function inversion problems. In: Kononov, A.V., Bykadorov, I.A., Khamisov, O.V., Davydov, I.A., Kononova, P.A. (eds.) Supplementary Proceedings of the 9th International Conference on Discrete Optimization and Operations Research and Scientific School (DOOR 2016). CEUR Workshop Proceedings, vol. 1623, pp. 261–275. CEUR-WS.org (2016)

    Google Scholar 

  63. Semenov, A., Zaikin, O.: Algorithm for finding partitionings of hard variants of Boolean satisfiability problem with application to inversion of some cryptographic functions. SpringerPlus 5(1), 1–16 (2016)

    Article  Google Scholar 

  64. Semenov, A.A., Zaikin, O., Bespalov, D., Posypkin, M.: Parallel logical cryptanalysis of the generator A5/1 in BNB-grid system. In: Malyshkin, V. (ed.) Parallel Computing Technologies - 11th International Conference, PaCT 2011. Lecture Notes in Computer Science, vol. 6873, pp. 473–483. Springer, Berlin (2011). https://doi.org/10.1007/978-3-642-23178-0_43

    MATH  Google Scholar 

  65. Semenov, A.A., Zaikin, O., Otpuschennikov, I.V., Kochemazov, S., Ignatiev, A.: On cryptographic attacks using backdoors for SAT. In: McIlraith, S.A., Weinberger, K.Q. (eds.) Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence (AAAI-18), pp. 6641–6648. AAAI Press, Palo Alto (2018)

    Google Scholar 

  66. Semenov, A., Otpuschennikov, I., Gribanova, I., Zaikin, O., Kochemazov, S.: Translation of algorithmic descriptions of discrete functions to SAT with applications to cryptanalysis problems. Log. Meth. Comput. Sci. 16, 29:1–29:42 (2020)

    Google Scholar 

  67. Soos, M.: Grain of Salt - an automated way to test stream ciphers through SAT solvers. In: Tools’10: Proceedings of the Workshop on Tools for Cryptanalysis, pp. 131–144 (2010)

    Google Scholar 

  68. Soos, M., Nohl, K., Castelluccia, C.: Extending SAT solvers to cryptographic problems. In: Kullmann, O. (ed.) Theory and Applications of Satisfiability Testing - SAT 2009, 12th International Conference, SAT 2009. Lecture Notes in Computer Science, vol. 5584, pp. 244–257. Springer, Berlin (2009). https://doi.org/10.1007/978-3-642-02777-2_24

    Google Scholar 

  69. Tseitin, G.S.: On the complexity of derivation in propositional calculus. In: A.O. Slisenko (ed.) Studies in Mathematics and Mathematical Logic, Part II, pp. 115–125. Steklov Mathematical Institute, Moscow (1968)

    Google Scholar 

  70. Wegener, I.: The Complexity of Boolean Functions. Wiley, Hoboken (1987)

    MATH  Google Scholar 

  71. Williams, R., Gomes, C.P., Selman, B.: Backdoors to typical case complexity. In: Gottlob, G., Walsh, T. (eds.) Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence, IJCAI-03, pp. 1173–1178. Morgan Kaufmann, Burlington (2003)

    Google Scholar 

  72. Zaikin, O.: SAT-based cryptanalysis: from parallel computing to volunteer computing. In: Voevodin, V.V., Sobolev, S. (eds.) Supercomputing - 5th Russian Supercomputing Days, RuSCDays 2019. Communications in Computer and Information Science, vol. 1129, pp. 701–712. Springer, Berlin (2019). https://doi.org/10.1007/978-3-030-36592-9_57

    Google Scholar 

  73. Zaikin, O., Kochemazov, S.: An improved SAT-based guess-and-determine attack on the alternating step generator. In: Nguyen, P.Q., Zhou, J. (eds.) Information Security - 20th International Conference, ISC 2017. Lecture Notes in Computer Science, vol. 10599, pp. 21–38. Springer, Berlin (2017). https://doi.org/10.1007/978-3-319-69659-1_2

    Google Scholar 

  74. Zaikin, O., Kochemazov, S.: Pseudo-boolean black-box optimization methods in the context of divide-and-conquer approach to solving hard SAT instances. In: OPTIMA 2018 (Supplementary Volume), pp. 76–87. DEStech Publications, Lancaster (2018)

    Google Scholar 

  75. Zaikin, O., Kochemazov, S.: On black-box optimization in divide-and-conquer SAT solving. Optimization Methods and Software pp. 1–25 (2019). https://doi.org/10.1080/10556788.2019.1685993

  76. Zhang, H., Bonacina, M.P., Hsiang, J.: PSATO: a distributed propositional prover and its application to quasigroup problems. J. Symb. Comput. 21(4), 543–560 (1996). https://doi.org/10.1006/jsco.1996.0030

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The research was funded by Russian Science Foundation (project No. 16-11-10046). Stepan Kochemazov is additionally supported by the Council for Grants of the President of the Russian Federation (stipend SP-2017.2019.5).

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  1. Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russia

    Alexander Semenov, Oleg Zaikin & Stepan Kochemazov

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  1. Department of Industrial & Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

  2. Moscow Aviation Institute, Moscow, Russia

    Varvara Rasskazova

  3. Mathematics Department, University of Patras, Patras, Greece

    Michael N. Vrahatis

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Semenov, A., Zaikin, O., Kochemazov, S. (2021). Finding Effective SAT Partitionings Via Black-Box Optimization. In: Pardalos, P.M., Rasskazova, V., Vrahatis, M.N. (eds) Black Box Optimization, Machine Learning, and No-Free Lunch Theorems. Springer Optimization and Its Applications, vol 170. Springer, Cham. https://doi.org/10.1007/978-3-030-66515-9_11

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