Skip to main content
SpringerLink
Log in

PRuning Through Satisfaction

  • Conference paper
  • First Online:
Hardware and Software: Verification and Testing (HVC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10629))

Included in the following conference series:

Abstract

The classical approach to solving the satisfiability problem of propositional logic prunes unsatisfiable branches from the search space. We prune more agressively by also removing certain branches for which there exist other branches that are more satisfiable. This is achieved by extending the popular conflict-driven clause learning (CDCL) paradigm with so-called \(\mathsf {PR}\) -clause learning. We implemented our new paradigm, named satisfaction-driven clause learning (SDCL), in the SAT solver Lingeling. Experiments on the well-known pigeon hole formulas show that our method can automatically produce proofs of unsatisfiability whose size is cubic in the number of pigeons while plain CDCL solvers can only produce proofs of exponential size.

Supported by the National Science Foundation under grant CCF-1526760 and by the Austrian Science Fund (FWF) under projects S11409-N23 and W1255-N23.

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

Access this chapter

Log in via an institution
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., Katsirelos, G., Simon, L.: A restriction of extended resolution for clause learning SAT solvers. In: Proceedings of the 24th AAAI Conference on Artificial Intelligence (AAAI 2010), pp. 15–20. AAAI Press (2010)

    Google Scholar 

  2. Biere, A.: Splatz, lingeling, plingeling, treengeling, YalSAT entering the SAT Competition 2016. In: Proceedings of SAT competition 2016 – Solver and Benchmark Descriptions. Dep. of Computer Science Series of Publications B, vol. B-2016-1, pp. 44–45. University of Helsinki (2016)

    Google Scholar 

  3. Cook, S.A.: A short proof of the pigeon hole principle using extended resolution. SIGACT News 8(4), 28–32 (1976)

    Article  Google Scholar 

  4. Haken, A.: The intractability of resolution. Theoretical Computer Science 39, 297–308 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  5. Heule, M.J.H., Biere, A.: Proofs for satisfiability problems. In: All about Proofs, Proofs for All (APPA), Math. Logic and Foundations, vol. 55. College Pub (2015)

    Google Scholar 

  6. Heule, M.J.H., Kiesl, B., Biere, A.: Short proofs without new variables. In: de Moura, L. (ed.) CADE 2017. LNCS (LNAI), vol. 10395, pp. 130–147. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63046-5_9

    Chapter  Google Scholar 

  7. Järvisalo, M., Heule, M.J.H., Biere, A.: Inprocessing rules. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS (LNAI), vol. 7364, pp. 355–370. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31365-3_28

    Chapter  Google Scholar 

  8. Kiesl, B., Seidl, M., Tompits, H., Biere, A.: Super-blocked clauses. In: Olivetti, N., Tiwari, A. (eds.) IJCAR 2016. LNCS (LNAI), vol. 9706, pp. 45–61. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40229-1_5

    Google Scholar 

  9. Kleine Büning, H., Kullmann, O.: Minimal unsatisfiability and autarkies. In: Handbook of Satisfiability, pp. 339–401. IOS Press (2009)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  11. Marques Silva, J.P., Sakallah, K.A.: GRASP: A search algorithm for propositional satisfiability. IEEE Trans. Computers 48(5), 506–521 (1999)

    Article  MathSciNet  Google Scholar 

  12. Monien, B., Speckenmeyer, E.: Solving satisfiability in less than \(2^n\) steps. Discrete Applied Mathematics 10(3), 287–295 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  13. 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), pp. 530–535. ACM (2001)

    Google Scholar 

  14. Nordström, J.: On the interplay between proof complexity and SAT solving. SIGLOG News 2(3), 19–44 (2015)

    Google Scholar 

  15. Sinz, C.: Towards an optimal CNF encoding of boolean cardinality constraints. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 827–831. Springer, Heidelberg (2005). https://doi.org/10.1007/11564751_73

    Chapter  Google Scholar 

  16. Sinz, C., Biere, A.: Extended resolution proofs for conjoining BDDs. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds.) CSR 2006. LNCS, vol. 3967, pp. 600–611. Springer, Heidelberg (2006). https://doi.org/10.1007/11753728_60

    Chapter  Google Scholar 

  17. Sörensson, N., Biere, A.: Minimizing learned clauses. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 237–243. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02777-2_23

    Chapter  Google Scholar 

  18. Tseitin, G.S.: On the complexity of derivation in propositional calculus. In: Automation of Reasoning: 2: Classical Papers on Computational Logic 1967–1970, pp. 466–483. Springer, Heidelberg (1983)

    Google Scholar 

  19. Urquhart, A.: The complexity of propositional proofs. In: Current Trends in Theoretical Computer Science, pp. 332–342. World Scientific (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, The University of Texas at Austin, Austin, USA

    Marijn J. H. Heule

  2. Institute of Information Systems, TU Wien, Vienna, Austria

    Benjamin Kiesl

  3. Institute for Formal Models and Verification, JKU Linz, Linz, Austria

    Martina Seidl & Armin Biere

Authors
  1. Marijn J. H. Heule
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Benjamin Kiesl
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Martina Seidl
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Armin Biere
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marijn J. H. Heule .

Editor information

Editors and Affiliations

  1. Technion - Israel Institute of Technology, Haifa, Israel

    Ofer Strichman

  2. IBM Research Lab, Haifa, Israel

    Rachel Tzoref-Brill

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Heule, M.J.H., Kiesl, B., Seidl, M., Biere, A. (2017). PRuning Through Satisfaction. In: Strichman, O., Tzoref-Brill, R. (eds) Hardware and Software: Verification and Testing. HVC 2017. Lecture Notes in Computer Science(), vol 10629. Springer, Cham. https://doi.org/10.1007/978-3-319-70389-3_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-70389-3_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70388-6

  • Online ISBN: 978-3-319-70389-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation