New Results on the Phase Transition for Random Quantified Boolean Formulas | SpringerLink
Skip to main content

New Results on the Phase Transition for Random Quantified Boolean Formulas

  • Conference paper
Theory and Applications of Satisfiability Testing – SAT 2008 (SAT 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4996))

Abstract

The QSAT problem is the quantified version of the satisfiability problem SAT. We study the phase transition associated with random QSAT instances. We focus on a certain subclass of closed quantified Boolean formulas that can be seen as quantified extended 2-CNF formulas. The evaluation problem for this class is coNP-complete. We carry out an advanced practical and theoretical study, which illuminates the influence of the different parameters used to define random quantified instances.

This work has been supported by EGIDE 10632SE, ÖAD Amadée 2/2006 and ACI NIM 202.

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

Access this chapter

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 5719
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 7149
Price includes VAT (Japan)
  • 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.

Similar content being viewed by others

References

  1. Aspvall, B., Plass, M.F., Tarjan, R.E.: A linear-time algorithm for testing the truth of certain quantified Boolean formulas. Information Processing Letters 8(3), 121–123 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  2. Chen, H., Interian, Y.: A model for generating random quantified Boolean formulas. In: Proceedings of the 19th International joint Conference on Artificial Intelligence, IJCAI 2005, pp. 66–71 (2005)

    Google Scholar 

  3. Chvátal, V., Reed, B.: Mick gets some (the odds are on his side). In: Proceedings of the 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992, pp. 620–627 (1992)

    Google Scholar 

  4. Creignou, N., Daudé, H., Dubois, O.: Expected number of locally maximal solutions for random Boolean CSPs. In: Proceedings of the13th International Conference on Analysis of Algorithms, AofA 2007, Antibes, June 2007. DMTCS, pp. 507–516 (2007)

    Google Scholar 

  5. Creignou, N., Daudé, H., Egly, U.: Phase transition for random quantified XOR-formulas. Journal of Artificial Intelligence Research 19, 1–18 (2007)

    Google Scholar 

  6. Dubois, O., Boufkhad, Y.: A general upper bound for the satisfiability threshold of random r-SAT formulae. Journal of Algorithms 24(2), 395–420 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Flögel, A., Karpinski, M., Kleine Büning, H.: Subclasses of quantified Boolean formulas. In: Schönfeld, W., Börger, E., Kleine Büning, H., Richter, M.M. (eds.) CSL 1990. LNCS, vol. 533, pp. 145–155. Springer, Heidelberg (1991)

    Google Scholar 

  8. Gent, I.P., Walsh, T.: Beyond NP: the QSAT phase transition. In: Proceedings of AAAI 1999 (1999)

    Google Scholar 

  9. Giunchiglia, E., Narizzano, M., Tacchella, A.: QuBE: A System for Deciding Quantified Boolean Formulas Satisfiability. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 364–369. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  10. Goerdt, A.: A threshold for unsatisfiability. Journal of of Computer and System Sciences 53(3), 469–486 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  11. Interian, Y., Corvera, G., Selman, B., Williams, R.: Finding small unsatisfiable cores to prove unsatisfiability of QBFs. In: Proceedings of the 9th International Symposium on Artificial Intelligence and Mathematics (2006)

    Google Scholar 

  12. Temme, N.M.: Asymptotic estimates of Stirling numbers. Stud. appl. Math. 89, 223–243 (1993)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Hans Kleine Büning Xishun Zhao

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Creignou, N., Daudé, H., Egly, U., Rossignol, R. (2008). New Results on the Phase Transition for Random Quantified Boolean Formulas. In: Kleine Büning, H., Zhao, X. (eds) Theory and Applications of Satisfiability Testing – SAT 2008. SAT 2008. Lecture Notes in Computer Science, vol 4996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79719-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-79719-7_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79718-0

  • Online ISBN: 978-3-540-79719-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics