Skip to main content
Log in

Undecidable statements and random graphs

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

Abstract

In this paper we will consider random graphsG n,p ,p=n α a rational number between 0 and 1. We show that there is no decision procedure that separates those first order statements that hold almost always inG n,p from those whose negation holds almost always.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. B. Bollobás,Random Graphs (Academic Press, New York, 1985).

    Google Scholar 

  2. H. Chernoff, A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations, Ann. Math. Stat. 23 (1952) 493–507.

    Google Scholar 

  3. D. Matula, Expose-and-merge exploration and the chromatic number of a random graph, Combinatorica 7 (1987) 275–284.

    Google Scholar 

  4. E.M. Palmer,Graphical Evolution (Wiley, New York, 1985).

    Google Scholar 

  5. A. Rényi,Probability Theory (Akadémiai Kiadó, Budapest, 1970).

    Google Scholar 

  6. S. Shelah and J. Spencer, Zero-one laws for sparse random graphs, J. Amer. Math. Soc. 1 (1988) 97–115.

    Google Scholar 

  7. J. Spencer,Ten Lectures on the Probabilistic Method (Society for Industrial and Applied Mathematics, Philadelphia, 1987).

    Google Scholar 

  8. B.A. Trachtenbrot, Impossibility of an algorithm for the decision problem on finite classes, Doklady Akad. Nauk. S.S.R. 70 (1950) 569–572.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dolan, P. Undecidable statements and random graphs. Ann Math Artif Intell 6, 17–25 (1992). https://doi.org/10.1007/BF01531021

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01531021

Keywords

Navigation