Skip to main content
SpringerLink
Log in

The equivalence of Horn and network complexity for Boolean functions

  • Published:
Acta Informatica Aims and scope Submit manuscript

Summary

We propose in this paper a logical complexity measure — Horn complexity — for Boolean functions which measures the minimal length of quasi-Horn definitions of such functions by propositional formulae. The interest for this complexity measure comes on the one hand from the observation that the satisfiability problem for Horn formulae is in P, on the other hand from a strong connection to Cook's problem. We show the proposed Horn complexity to be polynomially equivalent to network complexity and therefore to Turing complexity for Boolean functions.

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

Access this article

Log in via an institution

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

References

  1. Aanderaa, A.O.: On the decision problem for formulas in which all disjunctions are binary. Proc. of the Second Scand. Log. Symp. Amsterdam: North Holland pp. 1–18 (1971)

    Google Scholar 

  2. Börger, E.: Reduktionstypen in Krom- und Hornformeln. Dissertation, Münster. Arch. Math. Logik Grundlagenforsch. 16, 67–84 (1974)

    Google Scholar 

  3. Cook, S.A.: The complexity of theorem proving procedure. Conf. Rec. of 3rd ACM Symp. on Theory of Computing 151–158 (1970)

  4. Jones, N.D., Laaser, W.T.: Complete problems for deterministic polynomial time. Theor. Comput. Sci. 3, 105–117 (1977)

    Google Scholar 

  5. Schnorr, C.P.: Rekursive Funktionen und ihre Komplexität. Stuttgart: Teubner (1974)

    Google Scholar 

  6. Schnorr, C.P.: The network complexity and the Turing machine complexity of finite functions. Acta Informat. 7, 95–107 (1976)

    Google Scholar 

  7. Schnorr, C.P.: The network complexity and the breadth of Boolean functions. In: (R.O. Gandy, J.M.E. Hyland, Eds.): Logic Colloquium 76. Amsterdam: North Holland. 1977

    Google Scholar 

  8. Shoenfield, J.R.: Mathematical logic. Reading, MA: Addison-Wesley, 1967

    Google Scholar 

  9. Specker, E., Strassen, V. (Hrsg.): Komplexität von Entscheidungsproblemen. Lecture Notes in Computer Science, Vol. 43. Berlin Heidelberg New York: Springer, 1976

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Matematisk Institutt, Universitetet i Oslo, Blindern, Oslo, Norway

    Stal O. Anderaa

  2. Lehrstuhl Informatik II, Universität Dortmund, Postfach 500500, 4600, Dortmund 50, Germany (Fed. Rep.)

    Egon Börger

Authors
  1. Stal O. Anderaa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Egon Börger
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

A preliminary version of this work has appeared in the Proceedings of the 5th Scandinavian Logic Symposium, edited by B. Mayoh and F. Jensen, Aalborg University Press, Aalborg 1979

Rights and permissions

Reprints and permissions

About this article

Cite this article

Anderaa, S.O., Börger, E. The equivalence of Horn and network complexity for Boolean functions. Acta Informatica 15, 303–307 (1981). https://doi.org/10.1007/BF00289267

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00289267

Keywords

Search

Navigation