[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Boolean Functions as Models for Quantified Boolean Formulas

  • Published:
Journal of Automated Reasoning Aims and scope Submit manuscript

Abstract

In this paper, we introduce the notion of models for quantified Boolean formulas. For various classes of quantified Boolean formulas and various classes of Boolean functions, we investigate the problem of determining whether a model exists. Furthermore, we show for these classes the complexity of the model checking problem, which is to check whether a given set of Boolean functions is a model for a formula. For classes of Boolean functions, we establish some characterizations in terms of classes of quantified Boolean formulas that have such a model.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Aspvall, B., Plass, M.F., Tarjan, R.E.: A Linear-time algorithm for testing the truth of certain quantified Boolean formulas. Inf. Process. Lett. 8, 121–123 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  2. Cadoli, M., Schaerf, M., Giovanardi, A., Giovanardi, M.: An algorithm to evaluate quantified Boolean formulas and its evaluation. In: Highlights of Satisfiability Research in the Year 2000. IOS, Amsterdam (2000)

  3. Flögel, A., Karpinski, M., Kleine Büning, H.: Resolution for quantified Boolean formulas. Information and Computation. 117, 12–18 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  4. Feldmann, R., Monien, B., Schambergers, S.: A distributed algorithm to evaluate quantified Boolean formulas. In: Proceedings of AAAI (2000)

  5. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)

    Google Scholar 

  6. Giunchiglia, E., Narizzano, M., Tacchella, A.: QuBE: a system for deciding quantified Boolean formulas. In: Proceedings of IJCAR, Siena (2001)

  7. Haken, A.: The intractability of resolution. Theor. Comp. Sci. 39, 297–308 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kleine Büning, H., Lettmann, T.: Propositional Logic: Deduction and Algorithms. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  9. Kleine Büning, H., Subramani, K., Zhao, X.: On Boolean models for quantified Boolean horn formulas. SAT 2003, Italy. Lect. Notes Comput. Sci. 2919, 93–104 (2004)

    Article  Google Scholar 

  10. Letz, R.: Advances in decision procedure for quantified Boolean formulas. In: Proceedings of IJCAR, Siena (2001)

  11. Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, New York (1994)

    MATH  Google Scholar 

  12. Rintanen, J.T.: Improvements to the evaluation of quantified Boolean formulae. In: Proceedings of IJCAI (1999)

  13. Stockmeyer, L.J.: The polynomial-time hierarchy. Theor. Comp. Sci. 3, 1–22 (1977)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Universität Paderborn, 33095, Paderborn, Germany

    Hans Kleine Büning

  2. LDCSEE, West Virginia University, Morgantown, WV, 26506, USA

    K. Subramani

  3. Institute of Logic and Cognition, Sun Yat-sen University, 510275, Guangzhou, People’s Republic of China

    Xishun Zhao

Authors
  1. Hans Kleine Büning
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Subramani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xishun Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hans Kleine Büning.

Additional information

This research has been supported in part by the Air Force Office of Scientific Research under grant FA9550-06-1-0050.

This research has been supported in part by the NSFC under grants 60573011 and 10410638.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kleine Büning, H., Subramani, K. & Zhao, X. Boolean Functions as Models for Quantified Boolean Formulas. J Autom Reasoning 39, 49–75 (2007). https://doi.org/10.1007/s10817-007-9067-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10817-007-9067-0

Keywords

Search

Navigation