Skip to main content
SpringerLink
Log in

The cutting plane proof system with bounded degree of falsity

  • Conference paper
  • First Online:
Computer Science Logic (CSL 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 626))

Included in the following conference series:

Abstract

The cutting plane proof system for proving the unsatisfiability of propositional formulas in conjunctive normalform is based on a natural representation of formulas as systems of integer inequalities. We define a restriction of this system, the cutting plane system with bounded degree of falsity, and show the results: This system p-simulates resolution and has polynomial size proofs for the pigeonhole formulas. The formulas from [ 9] only have superpolynomially long proofs in the system. Our system is the only known system with provably superpolynomial proof size, but polynomial size proofs for the pigeonhole formulas.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Ajtai, The complexity of the pigeonhole principle, Proceedings of the 29th Symposium on Foundations of Computer Science (1988).

    Google Scholar 

  2. S. Buss, Polynomial size proofs of the propositional pigeonhole principle, Journ. Symb. Logic 52 (1987) pp.916–927.

    Google Scholar 

  3. C.-L. Chang, R.C.-T. Lee, Symbolic Logic and mechanical theorem proving, Academic Press (1973).

    Google Scholar 

  4. P. Clote, Bounded arithmetic and computational complexity, Proceedings Structures in Complexity (1990) pp. 186–199.

    Google Scholar 

  5. W. Cook, C.R. Coullard, G. Turan, On the complexity of cutting plane proofs, Discr. Appl. Math. 18 (1987) pp. 25–38.

    Google Scholar 

  6. S. A. Cook, R.A. Reckhow, The relative efficiency of propositional proof systems, Journ. Sym. Logic 44 (1979) pp. 36–50.

    Google Scholar 

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

    Google Scholar 

  8. A. Goerdt, Cutting plane versus Frege proof systems, CSL (1990) LNCS 533, pp. 174–194.

    Google Scholar 

  9. A. Urquhart, Hard examples for resolution, JACM 34 (1) (1987) pp. 209–219.

    Google Scholar 

  10. R.A. Smullyan, First-order Logic, Springer Verlag (1968).

    Google Scholar 

  11. V. Chvatal, Probabilistic methods in graph theory, Annals of Operations Research 1 (1984) pp. 171–182.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FB 17 Mathematik/Informatik, Universität -GH- Paderborn, Warburger Straße 100, Postfach 1621, D-W-4790, Paderborn, Germany

    Andreas Goerdt

Authors
  1. Andreas Goerdt
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Egon Börger Gerhard Jäger Hans Kleine Büning Michael M. Richter

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Goerdt, A. (1992). The cutting plane proof system with bounded degree of falsity. In: Börger, E., Jäger, G., Kleine Büning, H., Richter, M.M. (eds) Computer Science Logic. CSL 1991. Lecture Notes in Computer Science, vol 626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023762

Download citation

  • DOI: https://doi.org/10.1007/BFb0023762

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55789-0

  • Online ISBN: 978-3-540-47285-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation