Advertisement

Blocked Literals Are Universal

  • Marijn  J. H. Heule
  • Martina Seidl
  • Armin Biere
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9058)

Abstract

We recently introduced a new proof system for Quantified Boolean Formulas (QBF), called QRAT, that opened up a variety of new preprocessing techniques. This paper presents a concept that follows from the QRAT proof system: blocked literals. Blocked literals are redundant universal literals that can be removed or added to clauses. We show that blocked literal elimination (BLE) and blocked literal addition are not confluent. We implemented BLE in the state-of-the-art preprocessor bloqqer. Our experimental results illustrate that the BLE extension improves solver performance on the 2014 QBF evaluation benchmarks.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Heule, M.J.H., Seidl, M., Biere, A.: A unified proof system for QBF preprocessing. In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS, vol. 8562, pp. 91–106. Springer, Heidelberg (2014) Google Scholar
  2. 2.
    Cadoli, M., Schaerf, M., Giovanardi, M., Giovanardi, M.: An algorithm to evaluate quantified boolean formulae and its experimental evaluation. Journal of Automated Reasoning, 262–267 (1999)Google Scholar
  3. 3.
    Biere, A., Lonsing, F., Seidl, M.: Blocked clause elimination for QBF. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 101–115. Springer, Heidelberg (2011) Google Scholar
  4. 4.
    Tseitin, G.S.: On the complexity of derivation in propositional calculus. In: Automation of Reasoning 2, pp. 466–483. Springer (1983)Google Scholar
  5. 5.
    Ansótegui, C., Gomes, C.P., Selman, B.: The Achilles’ Heel of QBF. In: AAAI 2005, pp. 275–281. AAAI Press / The MIT Press (2005)Google Scholar
  6. 6.
    Heule, M.J.H., Seidl, M., Biere, A.: Efficient Extraction of Skolem Functions from QRAT Proofs. In: FMCAD 2014, pp. 107–114. IEEE (2014)Google Scholar
  7. 7.
    Heule, M.J.H., Järvisalo, M., Biere, A.: Clause elimination procedures for CNF formulas. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 357–371. Springer, Heidelberg (2010) Google Scholar
  8. 8.
    Heule, M.J.H., Järvisalo, M., Biere, A.: Covered clause elimination. In: LPAR-17-short. EPiC Series, vol. 13, pp. 41–46. EasyChair (2013)Google Scholar
  9. 9.
    Biere, A.: Resolve and expand. In: H. Hoos, H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 59–70. Springer, Heidelberg (2005) Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Marijn  J. H. Heule
    • 1
  • Martina Seidl
    • 2
  • Armin Biere
    • 2
  1. 1.Department of Computer ScienceThe University of Texas at AustinAustinUSA
  2. 2.Institute for Formal Models and VerificationJKU LinzLinzAustria

Personalised recommendations