Skip to main content

Soundness of Inprocessing in Clause Sharing SAT Solvers

  • Conference paper
Theory and Applications of Satisfiability Testing – SAT 2013 (SAT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7962))

Abstract

We present a formalism that models the computation of clause sharing portfolio solvers with inprocessing. The soundness of these solvers is not a straightforward property since shared clauses can make a formula unsatisfiable. Therefore, we develop characterizations of simplification techniques and suggest various settings how clause sharing and inprocessing can be combined. Our formalization models most of the recent implemented portfolio systems and we indicate possibilities to improve these. A particular improvement is a novel way to combine clause addition techniques – like blocked clause addition – with clause deletion techniques – like blocked clause elimination or variable elimination.

The second author was supported by the European Master’s Program in Computational Logic (EMCL).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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)

    Chapter  Google Scholar 

  2. Audemard, G., Hoessen, B., Jabbour, S., Lagniez, J.M., Piette, C.: Penelope, a parallel clause-freezer solver. In: SAT Challenge 2012; Solver and Benchmark Descriptions, pp. 43–44 (2012)

    Google Scholar 

  3. 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)

    Chapter  Google Scholar 

  4. Audemard, G., Simon, L.: Predicting learnt clauses quality in modern SAT solvers. In: Proc. 21st Int. Joint Conf. on Artifical Intelligence (IJCAI 2009), pp. 399–404. Morgan Kaufmann (2009)

    Google Scholar 

  5. Beame, P., Kautz, H., Sabharwal, A.: Towards understanding and harnessing the potential of clause learning. Journal of Artificial Intelligence Research 22(1), 319–351 (2004)

    MathSciNet  MATH  Google Scholar 

  6. Biere, A.: Lingeling, Plingeling, PicoSAT and PrecoSAT at SAT Race 2010. FMV Report Series Technical Report 10/1, Johannes Kepler University, Linz, Austria (2010)

    Google Scholar 

  7. Biere, A., Cimatti, A., Clarke, E.M., Fujita, M., Zhu, Y.: Symbolic model checking using SAT procedures instead of BDDs. In: Proc. 36th Annual ACM/IEEE Design Automation Conf (DAC), pp. 317–320. ACM (1999)

    Google Scholar 

  8. Böhm, M., Speckenmeyer, E.: A fast parallel SAT-solver – efficient workload balancing. Annals of Mathematics and Artificial Intelligence 17, 381–400 (1996), (Based on a technical report published already in 1994)

    Google Scholar 

  9. Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. CACM 5(7), 394–397 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  10. Eén, N., Biere, A.: Effective preprocessing in SAT through variable and clause elimination. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 61–75. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. 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)

    Chapter  Google Scholar 

  12. Gelder, A.V.: Toward leaner binary-clause reasoning in a satisfiability solver. Annals of Mathematics and Artificial Intelligence 43(1), 239–253 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Gomes, C.P., Selman, B., Crato, N., Kautz, H.: Heavy-tailed phenomena in satisfiability and constraint satisfaction problems. Journal of Automated Reasoning 24(1-2), 67–100 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  14. Großmann, P., Hölldobler, S., Manthey, N., Nachtigall, K., Opitz, J., Steinke, P.: Solving periodic event scheduling problems with SAT. In: Jiang, H., Ding, W., Ali, M., Wu, X. (eds.) IEA/AIE 2012. LNCS, vol. 7345, pp. 166–175. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  15. 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)

    Chapter  Google Scholar 

  16. Hamadi, Y., Jabbour, S., Piette, C., Sais, L.: Deterministic parallel DPLL. JSAT 7(4), 127–132 (2011)

    MathSciNet  Google Scholar 

  17. Hamadi, Y., Jabbour, S., Sais, L.: Control-based clause sharing in parallel SAT solving. In: Proc. 21st Int. Joint Conf. on Artificial Intelligence (IJCAI 2009), pp. 499–504 (2009)

    Google Scholar 

  18. Hamadi, Y., Jabbour, S., Sais, L.: ManySAT: a parallel SAT solver. JSAT 6(4), 245–262 (2009)

    MATH  Google Scholar 

  19. 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)

    Chapter  Google Scholar 

  20. Heule, M.J.H., Järvisalo, M., Biere, A.: Efficient CNF simplification based on binary implication graphs. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 201–215. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  21. Hölldobler, S., Manthey, N., Nguyen, V., Stecklina, J., Steinke, P.: A short overview on modern parallel SAT-solvers. In: Proc. Int. Conf. on Advanced Computer Science and Information Systems (ICACSIS 2011), pp. 201–206. IEEE (2011)

    Google Scholar 

  22. 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)

    Chapter  Google Scholar 

  23. Hyvärinen, A.E.J., Manthey, N.: Designing scalable parallel SAT solvers. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 214–227. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  24. Hyvärinen, A.E.J., Junttila, T., Niemelä, I.: Grid-based SAT solving with iterative partitioning and clause learning. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 385–399. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  25. Järvisalo, M., Biere, A., Heule, M.J.H.: Blocked clause elimination. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 129–144. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  26. Järvisalo, M., Heule, M.J.H., Biere, A.: Inprocessing rules. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 355–370. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  27. Katebi, H., Sakallah, K.A., Marques-Silva, J.P.: Empirical study of the anatomy of modern SAT solvers. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 343–356. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  28. Kullmann, O.: On a generalization of extended resolution. Discrete Applied Mathematics 96- 97(1), 149–176 (1999)

    Article  Google Scholar 

  29. Lanti, D., Manthey, N.: Sharing information in parallel search with search space partitioning. In: Learning and Intelligent Optimization – 7th Int. Conf. (LION 7) (to appear, 2013)

    Google Scholar 

  30. Lynce, I., Marques-Silva, J.P.: Probing-based preprocessing techniques for propositional satisfiability. In: Proc. 15th IEEE Int. Conf. on Tools with Artificial Intelligence (ICTAI 2003), pp. 105–110. IEEE (2003)

    Google Scholar 

  31. Manthey, N.: Coprocessor 2.0 – A flexible CNF simplifier. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 436–441. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  32. Manthey, N., Heule, M.J.H., Biere, A.: Automated reencoding of Boolean formulas. In: Hardware and Software: Verification and Testing – 8th Int. Haifa Verification Conf. (HVC 2012). LNCS, Springer (to appear, 2013)

    Google Scholar 

  33. Marques-Silva, J.P., Sakallah, K.A.: Grasp: A search algorithm for propositional satisfiability. IEEE Transactions on Computers 48(5), 506–521 (1999)

    Article  MathSciNet  Google Scholar 

  34. Martins, R., Manquinho, V., Lynce, I.: An overview of parallel SAT solving. Constraints 17(3), 304–347 (2012)

    Article  MathSciNet  Google Scholar 

  35. Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: Proc. 38th Annual ACM/IEEE Design Automation Conf. (DAC), pp. 530–535. ACM (2001)

    Google Scholar 

  36. Pipatsrisawat, K., Darwiche, A.: On the power of clause-learning SAT solvers as resolution engines. Artificial Intelligence 175(2), 512–525 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  37. Roussel, O.: Description of ppfolio 2012. In: Proc. SAT Challenge 2012; Solver and Benchmark Descriptions, p. 46. Univ. of Helsinki (2012), http://hdl.handle.net/10138/34218

  38. Soos, M.: Cryptominisat 2.5.0. In: SAT Race Competitive Event Booklet (July 2010), http://baldur.iti.uka.de/sat-race-2010/descriptions/solver_13.pdf (retrieved February 11, 2013)

  39. Sörensson, N., Biere, A.: Minimizing learned clauses. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 237–243. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  40. Subbarayan, S., Pradhan, D.K.: NiVER: Non-increasing variable elimination resolution for preprocessing SAT instances. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 276–291. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  41. Tseitin, G.S.: On the complexity of derivations in the propositional calculus. Studies in Mathematics and Mathematical Logic Part II, 115–125 (1968)

    Google Scholar 

  42. Wotzlaw, A., van der Grinten, A., Speckenmeyer, E., Porschen, S.: pfoliouzk: Solver description. In: Proc. SAT Challenge 2012; Solver and Benchmark Descriptions, p. 45. Univ. of Helsinki (2012), http://hdl.handle.net/10138/34218

  43. Zhang, H., Bonacina, M.P., Hsiang, J.: Psato: a distributed propositional prover and its application to quasigroup problems. Journal of Symbolic Computation 21(4), 543–560 (1996)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Manthey, N., Philipp, T., Wernhard, C. (2013). Soundness of Inprocessing in Clause Sharing SAT Solvers. In: Järvisalo, M., Van Gelder, A. (eds) Theory and Applications of Satisfiability Testing – SAT 2013. SAT 2013. Lecture Notes in Computer Science, vol 7962. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39071-5_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39071-5_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39070-8

  • Online ISBN: 978-3-642-39071-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics