Skip to main content

2016 | OriginalPaper | Buchkapitel

An Adaptive Parallel SAT Solver

verfasst von : Gilles Audemard, Jean-Marie Lagniez, Nicolas Szczepanski, Sébastien Tabary

Erschienen in: Principles and Practice of Constraint Programming

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We present and evaluate AmPharoS, a new parallel SAT solver based on the divide and conquer paradigm. This solver, designed to work on a great number of cores, runs workers on sub-formulas restricted to cubes. In addition to classical clause sharing, it also exchange extra information associated to the cubes. Furthermore, we propose a new criterion to dynamically adapt both the amount of shared clauses and the number of cubes. Experiments show that, in general, AmPharoS correctly adjusts its strategy to the nature of the problem. Thus, we show that our new parallel approach works well and opens a broad range of possibilities to boost parallel SAT solver performances.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Fußnoten
1
We will discuss about the definition of the extension factor in Sect. 5.2.
 
Literatur
1.
Zurück zum Zitat Audemard, G., Hoessen, B., Jabbour, S., Lagniez, J.-M., Piette, C.: Revisiting clause exchange in parallel SAT solving. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 200–213. Springer, Heidelberg (2012)CrossRef Audemard, G., Hoessen, B., Jabbour, S., Lagniez, J.-M., Piette, C.: Revisiting clause exchange in parallel SAT solving. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 200–213. Springer, Heidelberg (2012)CrossRef
2.
Zurück zum Zitat Audemard, G., Hoessen, B., Jabbour, S., Piette, C.: An effective distributed d&c approach for the satisfiability problem. In: 22nd Euromicro International Conference on Parallel, Distributed, and Network-Based Processing, PDP 2014, Torino, Italy, pp. 183–187, 12–14 February 2014 Audemard, G., Hoessen, B., Jabbour, S., Piette, C.: An effective distributed d&c approach for the satisfiability problem. In: 22nd Euromicro International Conference on Parallel, Distributed, and Network-Based Processing, PDP 2014, Torino, Italy, pp. 183–187, 12–14 February 2014
3.
Zurück zum Zitat Audemard, G., Lagniez, J.-M., Mazure, B., Saïs, L.: On freezing and reactivating learnt clauses. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 188–200. Springer, Heidelberg (2011)CrossRef Audemard, G., Lagniez, J.-M., Mazure, B., Saïs, L.: On freezing and reactivating learnt clauses. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 188–200. Springer, Heidelberg (2011)CrossRef
4.
Zurück zum Zitat Audemard, G., Lagniez, J.-M., Simon, L.: Improving glucose for incremental SAT solving with assumptions: application to MUS extraction. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 309–317. Springer, Heidelberg (2013)CrossRef Audemard, G., Lagniez, J.-M., Simon, L.: Improving glucose for incremental SAT solving with assumptions: application to MUS extraction. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 309–317. Springer, Heidelberg (2013)CrossRef
5.
Zurück zum Zitat Audemard, G., Lagniez, J.-M., Simon, L.: Just-in-time compilation of knowledge bases. In: Proceedings of the 23rd International Joint Conference on Artificial Intelligence, IJCAI 2013, Beijing, China, 3–9 August 2013 Audemard, G., Lagniez, J.-M., Simon, L.: Just-in-time compilation of knowledge bases. In: Proceedings of the 23rd International Joint Conference on Artificial Intelligence, IJCAI 2013, Beijing, China, 3–9 August 2013
6.
Zurück zum Zitat Audemard, G., Simon, L.: Predicting learnt clauses quality in modern SAT solvers. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence, IJCAI 2009, Pasadena, California, USA, pp. 399–404, 11–17 July 2009 Audemard, G., Simon, L.: Predicting learnt clauses quality in modern SAT solvers. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence, IJCAI 2009, Pasadena, California, USA, pp. 399–404, 11–17 July 2009
7.
Zurück zum Zitat Audemard, G., Simon, L.: Lazy clause exchange policy for parallel SAT solvers. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 197–205. Springer, Heidelberg (2014) Audemard, G., Simon, L.: Lazy clause exchange policy for parallel SAT solvers. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 197–205. Springer, Heidelberg (2014)
9.
Zurück zum Zitat Belov, A., Lynce, I., Marques-Silva, J.: Towards efficient MUS extraction. AI Commun. 25(2), 97–116 (2012)MathSciNetMATH Belov, A., Lynce, I., Marques-Silva, J.: Towards efficient MUS extraction. AI Commun. 25(2), 97–116 (2012)MathSciNetMATH
10.
Zurück zum Zitat 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)MATH 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)MATH
11.
Zurück zum Zitat Biere, A.: Bounded model checking. In: Biere et al. [10], Chap. 14, vol. 185, pp. 455–481, February 2009 Biere, A.: Bounded model checking. In: Biere et al. [10], Chap. 14, vol. 185, pp. 455–481, February 2009
12.
Zurück zum Zitat Biere, A.: Lingeling, Plingeling and Treengeling entering the SAT competition 2013. In: Proceedings of SAT Competition 2013, p. 51 (2013) Biere, A.: Lingeling, Plingeling and Treengeling entering the SAT competition 2013. In: Proceedings of SAT Competition 2013, p. 51 (2013)
13.
Zurück zum Zitat Biere, A.: Yet another local search solver and lingeling and friends entering the sat competition 2014. In: Proceedings of SAT Competition (2014) Biere, A.: Yet another local search solver and lingeling and friends entering the sat competition 2014. In: Proceedings of SAT Competition (2014)
14.
Zurück zum Zitat Chen, J.: Minisat bcd and abcdsat: solvers based on blocked clause decomposition. In: SAT RACE 2015 Solvers Description (2015) Chen, J.: Minisat bcd and abcdsat: solvers based on blocked clause decomposition. In: SAT RACE 2015 Solvers Description (2015)
15.
Zurück zum Zitat Chrabakh, W., Wolski, R.: The gridsat portal: a grid web-based portal for solving satisfiability problems using the national cyberinfrastructure. Concurrency Comput. Pract. Exp. 19(6), 795–808 (2007)CrossRef Chrabakh, W., Wolski, R.: The gridsat portal: a grid web-based portal for solving satisfiability problems using the national cyberinfrastructure. Concurrency Comput. Pract. Exp. 19(6), 795–808 (2007)CrossRef
16.
Zurück zum Zitat Chu, G., Stuckey, P.J., Harwood, A.: Pminisat: a parallelization of minisat 2.0. Technical report, SAT Race (2008) Chu, G., Stuckey, P.J., Harwood, A.: Pminisat: a parallelization of minisat 2.0. Technical report, SAT Race (2008)
17.
Zurück zum Zitat Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)CrossRef Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)CrossRef
18.
Zurück zum Zitat Feldman, Y., Dershowitz, N., Hanna, Z.: Parallel multithreaded satisfiability solver: design and implementation. Electron. Notes Theoret. Comput. Sci. 128(3), 75–90 (2005)CrossRef Feldman, Y., Dershowitz, N., Hanna, Z.: Parallel multithreaded satisfiability solver: design and implementation. Electron. Notes Theoret. Comput. Sci. 128(3), 75–90 (2005)CrossRef
19.
20.
Zurück zum Zitat Gomes, C.P., Selman, B., Kautz, H.A.: Boosting combinatorial search through randomization. In: Proceedings of the Fifteenth National Conference on Artificial Intelligence and Tenth Innovative Applications of Artificial Intelligence Conference, AAAI 1998, IAAI 1998, Madison, Wisconsin, USA, pp. 431–437, 26–30 July 1998 Gomes, C.P., Selman, B., Kautz, H.A.: Boosting combinatorial search through randomization. In: Proceedings of the Fifteenth National Conference on Artificial Intelligence and Tenth Innovative Applications of Artificial Intelligence Conference, AAAI 1998, IAAI 1998, Madison, Wisconsin, USA, pp. 431–437, 26–30 July 1998
21.
Zurück zum Zitat Guo, L., Hamadi, Y., Jabbour, S., Sais, L.: Diversification and intensification in parallel SAT solving. In: Cohen, D. (ed.) CP 2010. LNCS, vol. 6308, pp. 252–265. Springer, Heidelberg (2010)CrossRef Guo, L., Hamadi, Y., Jabbour, S., Sais, L.: Diversification and intensification in parallel SAT solving. In: Cohen, D. (ed.) CP 2010. LNCS, vol. 6308, pp. 252–265. Springer, Heidelberg (2010)CrossRef
22.
Zurück zum Zitat Guo, L., Lagniez, J.-M.: Dynamic polarity adjustment in a parallel SAT solver. In: IEEE 23rd International Conference on Tools with Artificial Intelligence, ICTAI 2011, Boca Raton, FL, USA, pp. 67–73, 7–9 November 2011 Guo, L., Lagniez, J.-M.: Dynamic polarity adjustment in a parallel SAT solver. In: IEEE 23rd International Conference on Tools with Artificial Intelligence, ICTAI 2011, Boca Raton, FL, USA, pp. 67–73, 7–9 November 2011
23.
Zurück zum Zitat Hamadi, Y., Jabbour, S., Sais, L.: Control-based clause sharing in parallel SAT solving. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence, IJCAI 2009, Pasadena, California, USA, pp. 499–504, 11–17 July 2009 Hamadi, Y., Jabbour, S., Sais, L.: Control-based clause sharing in parallel SAT solving. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence, IJCAI 2009, Pasadena, California, USA, pp. 499–504, 11–17 July 2009
24.
Zurück zum Zitat Hamadi, Y., Jabbour, S., Sais, L.: Manysat: a parallel SAT solver. JSAT 6(4), 245–262 (2009)MATH Hamadi, Y., Jabbour, S., Sais, L.: Manysat: a parallel SAT solver. JSAT 6(4), 245–262 (2009)MATH
25.
Zurück zum Zitat Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: guiding CDCL SAT solvers by lookaheads. In: Eder, K., Lourenço, J., Shehory, O. (eds.) HVC 2011. LNCS, vol. 7261, pp. 50–65. Springer, Heidelberg (2012)CrossRef Heule, M.J.H., Kullmann, O., Wieringa, S., Biere, A.: Cube and conquer: guiding CDCL SAT solvers by lookaheads. In: Eder, K., Lourenço, J., Shehory, O. (eds.) HVC 2011. LNCS, vol. 7261, pp. 50–65. Springer, Heidelberg (2012)CrossRef
26.
Zurück zum Zitat Hyvärinen, A.E.J., Junttila, T., Niemelä, I.: Partitioning SAT instances for distributed solving. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 372–386. Springer, Heidelberg (2010)CrossRef Hyvärinen, A.E.J., Junttila, T., Niemelä, I.: Partitioning SAT instances for distributed solving. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 372–386. Springer, Heidelberg (2010)CrossRef
27.
Zurück zum Zitat Järvisalo, M., Biere, A., Heule, M.: Blocked clause elimination. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 129–144. Springer, Heidelberg (2010)CrossRef Järvisalo, M., Biere, A., Heule, M.: Blocked clause elimination. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 129–144. Springer, Heidelberg (2010)CrossRef
28.
Zurück zum Zitat Lagniez, J.-M., Biere, A.: Factoring out assumptions to speed up MUS extraction. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 276–292. Springer, Heidelberg (2013)CrossRef Lagniez, J.-M., Biere, A.: Factoring out assumptions to speed up MUS extraction. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 276–292. Springer, Heidelberg (2013)CrossRef
29.
Zurück zum Zitat Le Berre, D.: Exploiting the real power of unit propagation lookahead. Electron. Notes Discrete Math. 9, 59–80 (2001)CrossRefMATH Le Berre, D.: Exploiting the real power of unit propagation lookahead. Electron. Notes Discrete Math. 9, 59–80 (2001)CrossRefMATH
30.
Zurück zum Zitat Marques-Silva, J., Sakallah, K.: GRASP - a new search algorithm for satisfiability. In: Proceedings of the 1996 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 1996, pp. 220–227 (1996) Marques-Silva, J., Sakallah, K.: GRASP - a new search algorithm for satisfiability. In: Proceedings of the 1996 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 1996, pp. 220–227 (1996)
31.
Zurück zum Zitat Martins, R., Manquinho, V.M., Lynce, I.: Improving search space splitting for parallel SAT solving. In: 22nd IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2010, Arras, France, vol. 1, pp. 336–343, 27–29 October 2010 Martins, R., Manquinho, V.M., Lynce, I.: Improving search space splitting for parallel SAT solving. In: 22nd IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2010, Arras, France, vol. 1, pp. 336–343, 27–29 October 2010
32.
Zurück zum Zitat Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: engineering an efficient SAT solver. In: Proceedings of the 38th Design Automation Conference, DAC 2001, Las Vegas, NV, USA, pp. 530–535. ACM, 18–22 June 2001 Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: engineering an efficient SAT solver. In: Proceedings of the 38th Design Automation Conference, DAC 2001, Las Vegas, NV, USA, pp. 530–535. ACM, 18–22 June 2001
33.
Zurück zum Zitat Nadel, A., Ryvchin, V.: Efficient SAT solving under assumptions. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 242–255. Springer, Heidelberg (2012)CrossRef Nadel, A., Ryvchin, V.: Efficient SAT solving under assumptions. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 242–255. Springer, Heidelberg (2012)CrossRef
34.
Zurück zum Zitat Pipatsrisawat, K., Darwiche, A.: A lightweight component caching scheme for satisfiability solvers. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 294–299. Springer, Heidelberg (2007)CrossRef Pipatsrisawat, K., Darwiche, A.: A lightweight component caching scheme for satisfiability solvers. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 294–299. Springer, Heidelberg (2007)CrossRef
35.
Zurück zum Zitat Rintanen, J.: Planning and SAT. In: Biere et al. [10], Chap. 15, vol. 185, pp. 483–504, February 2009 Rintanen, J.: Planning and SAT. In: Biere et al. [10], Chap. 15, vol. 185, pp. 483–504, February 2009
38.
Zurück zum Zitat Schubert, T., Lewis, M., Becker, B.: Pamiraxt: parallel SAT solving with threads and message passing. J. Satisfiability Boolean Model. Comput. 6(4), 203–222 (2009)MATH Schubert, T., Lewis, M., Becker, B.: Pamiraxt: parallel SAT solving with threads and message passing. J. Satisfiability Boolean Model. Comput. 6(4), 203–222 (2009)MATH
39.
Zurück zum Zitat Semenov, A., Zaikin, O.: Using monte carlo method for searching partitionings of hard variants of boolean satisfiability problem. In: Malyshkin, V. (ed.) PaCT 2015. LNCS, vol. 9251, pp. 222–230. Springer, Heidelberg (2015)CrossRef Semenov, A., Zaikin, O.: Using monte carlo method for searching partitionings of hard variants of boolean satisfiability problem. In: Malyshkin, V. (ed.) PaCT 2015. LNCS, vol. 9251, pp. 222–230. Springer, Heidelberg (2015)CrossRef
40.
Zurück zum Zitat 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)CrossRef 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)CrossRef
41.
Zurück zum Zitat van der Tak, P., Heule, M.J.H., Biere, A.: Concurrent cube-and-conquer. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 475–476. Springer, Heidelberg (2012)CrossRef van der Tak, P., Heule, M.J.H., Biere, A.: Concurrent cube-and-conquer. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 475–476. Springer, Heidelberg (2012)CrossRef
42.
Zurück zum Zitat Zhang, H., Bonacina, M.P., Hsiang, J.: Psato: a distributed propositional prover and its application to quasigroup problems. J. Symbolic Comput. 21(4), 543–560 (1996)MathSciNetCrossRefMATH Zhang, H., Bonacina, M.P., Hsiang, J.: Psato: a distributed propositional prover and its application to quasigroup problems. J. Symbolic Comput. 21(4), 543–560 (1996)MathSciNetCrossRefMATH
Metadaten
Titel
An Adaptive Parallel SAT Solver
verfasst von
Gilles Audemard
Jean-Marie Lagniez
Nicolas Szczepanski
Sébastien Tabary
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-44953-1_3

Premium Partner