Skip to main content

Optimal Satisfiability for Propositional Calculi and Constraint Satisfaction Problems

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1893))

Abstract

We consider the problems of finding the lexicographically minimal (or maximal) satisfying assignment of propositional formulas for different restricted classes of formulas. It turns out that for each class from our framework, these problems are either polynomial time solvable or complete for OptP.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. N. Creignou and M. Hermann. Complexity of generalized satisfiability counting problems. Information and Computation, 125:1–12, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  2. N. Creignou and J.-J. Hébrard. On generating all solutions of generalized satisfiability problems. Informatique Théorique et Applications/Theoretical Informatics and Applications, 31(6):499–511, 1997.

    MATH  Google Scholar 

  3. N. Creignou, S. Khanna, and M. Sudan. Complexity Classifications of Boolean Constraint Satisfaction Problems. Monographs on Discrete Applied Mathematics. SIAM, 2000. To appear.

    Google Scholar 

  4. N. Creignou. A dichotomy theorem for maximum generalized satisfiability problems. Journal of Computer and System Sciences, 51:511–522, 1995.

    Article  MathSciNet  Google Scholar 

  5. S. W. Jablonski, G. P. Gawrilow, and W. B. Kudrajawzew. Boolesche Funktionen und Postsche Klassen. Akademie-Verlag, 1970.

    Google Scholar 

  6. L. Kirousis and P. G. Kolaitis. Dichotomy theorems for minimal satisfiability, manuscript, 1999.

    Google Scholar 

  7. M. W. Krentel. The complexity of optimization functions. Journal of Computer and System Sciences, 36:490–509, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. W. Krentel. Generalizations of OptP to the polynomial hierarchy. Theoretical Computer Science, 97:183–198, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  9. S. Khanna, M. Sudan, and L. Trevisan. Constraint satisfaction: The approximability of minimization problems. In Proceedings 12th Computational Complexity Conference, pages 282–296. IEEE Computer Society Press, 1997.

    Google Scholar 

  10. S. Khanna, M. Sudan, and D. Williamson. A complete classification of the approximability of maximization problems derived from boolean constraint satisfaction. In Proceedings 29th Symposium on Theory of Computing, pages 11–20. ACM Press, 1997.

    Google Scholar 

  11. R. Ladner. On the structure of polynomial-time reducibility. Journal of the ACM, 22:155–171, 1975.

    Article  MATH  MathSciNet  Google Scholar 

  12. Harry R. Lewis. Satisfiability problems for propositional calculi. Mathematical Systems Theory, 13:45–53, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  13. E. L. Post. The Two-Valued Iterative Systems of Mathematical Logic. Annals of Mathematics Studies 5. Princeton University Press, London, 1941.

    MATH  Google Scholar 

  14. Steffen Reith and Klaus W. Wagner. The complexity of problems defined by boolean circuits. Technical Report 255, Institut für Informatik, Universität Würzburg, 2000. To appear in Proceedings International Conference Mathematical Foundation of Informatics, Hanoi, October 25–28, 1999.

    Google Scholar 

  15. T. J. Schaefer. The complexity of satisfiability problems. In Proccedings 10th Symposium on Theory of Computing, pages 216–226. ACM Press, 1978.

    Google Scholar 

  16. K. W. Wagner. More complicated questions about maxima and minima, and some closures of NP. Theoretical Computer Science, 51:53–80, 1987.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Reith, S., Vollmer, H. (2000). Optimal Satisfiability for Propositional Calculi and Constraint Satisfaction Problems. In: Nielsen, M., Rovan, B. (eds) Mathematical Foundations of Computer Science 2000. MFCS 2000. Lecture Notes in Computer Science, vol 1893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44612-5_59

Download citation

  • DOI: https://doi.org/10.1007/3-540-44612-5_59

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67901-1

  • Online ISBN: 978-3-540-44612-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics