Skip to main content
Springer Nature Link
Log in

Davis-Putnam resolution versus unrestricted resolution

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

A resolution proof of an unsatisfiable propositional formula in conjunctive normal form is a “Davis-Putnam resolution proof” iff there exists a sequence of the variables of the formula such thatx is eliminated (with the resolution rule) beforey on any branch of the proof tree representing the resolution proof, only ifx is beforey in this sequence. Davis-Putnam resolution is one of several resolution restrictions. It is complete.

We present an infinite family of unsatisfiable propositional formulas and show: These formulas have unrestricted resolution proofs whose length is polynomial in their size. All Davis-Putnam resolution proofs of these formulas are of superpolynomial length. In the terminology of [4, definition 1.5]: Davis-Putnam resolution does notp-simulate unrestricted resolution.

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
$34.99 /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 excludes VAT (USA)
Tax calculation will be finalised during checkout.

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. M. Ajtai, The complexity of the propositional pigeonhole principle,Proc. 29th IEEE Symp. on Foundations of Computer Science (1988) p. 346–355.

  2. S.R. Buss and G. Turán, Resolution proofs of generalized pigeonhole principles, Theor. Comput. Sci. 62 (1988) 311–317.

    Google Scholar 

  3. V. Chvátal and E. Szemeredi, Many hard examples for resolution, J. ACM 35 (1988) 759–768.

    Google Scholar 

  4. S.A. Cook and R.A. Reckhow, The relative efficiency of propositional proof systems, J. Symbolic Logic 44(1) (1979) 36–50.

    Google Scholar 

  5. M. Davis and H. Putnam, A computing procedure for quantification theory, J. ACM 7 (1960) 201–215.

    Google Scholar 

  6. Z. Galil, On the complexity of regular resolution and the Davis-Putnam procedure, Theor. Comput. Sci. 4 (1977) 23–46.

    Google Scholar 

  7. A. Goerdt, Unrestricted resolution versusN-resolution, Theor. Comput. Sci., to appear.

  8. A. Haken, The intractability of resolution, Theor. Comput. Sci. 39 (1985) 297–308.

    Google Scholar 

  9. R.A. Reckhow, On the lengths of proofs in the propositional calculus, Ph. D. thesis, University of Toronto (1975).

  10. A. Urquhart, Hard examples for resolution, J. ACM 34 (1987) 209–219.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Fachgebiet Praktische Informatik, Universität -GH- Duisburg, Lotharstraße 65, D-4100, Duisburg, Germany

    Andreas Goerdt

Authors
  1. Andreas Goerdt
    View author publications

    You can also search for this author inPubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goerdt, A. Davis-Putnam resolution versus unrestricted resolution. Ann Math Artif Intell 6, 169–184 (1992). https://doi.org/10.1007/BF01531027

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01531027

Keywords