Skip to main content
SpringerLink
Log in

Are lower bounds on the complexity lower bounds for universal circuits?

Preliminary version

  • Conference paper
  • First Online:
Fundamentals of Computation Theory (FCT 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 199))

Included in the following conference series:

Abstract

An interpretation of lower bounds proofs as proofs of lower bounds on the universal circuits is presented. This interpretation is displayed on representative proof samples from [1,3,7 – 10]. It enables one to explain the difficulty of proving lower bounds and to forecast possibilities of proving high lower bounds for arbitrary computational model.

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. N. Blum. A Boolean function requiring 3n network size. Theor. Comp. Sci. 28 (1984) 337–345.

    Google Scholar 

  2. M.Furst, J.B.Saxe, M.Sipser. Parity, circuits and the polynomial time hierarchy. Proc. 22nd IEEE Symp. on Found. Comp. Sci. (1981) 260–270.

    Google Scholar 

  3. S.E. Kuznetsov. Combinational circuits with no null chains over basis {& V,−} (in Russian). Izvestija VUZ. Matematika 5 (1981) 56–63.

    Google Scholar 

  4. O.B. Lupanov. Implementing the algebra of logic functions in terms of bounded depth formulas in the basis {&, V, −}. Dokl. Akad. Nauk SSSR 136, No. 5; English translation in Sov. Phys.-Dokl. 6, No. 2 (1961).

    Google Scholar 

  5. E.I. Nechiporuck. On a Boolean function. Dokl. Akad. Nauk SSSR 169 (1966) 765–766; English translation in Sov. Math.-Dokl. 7, No. 4 (1966).

    Google Scholar 

  6. R.G. Nigmatullin. The complexity of universal functions and lower bounds on the complexity (in Russian). Izvestija VUZ. Matematika 11 (1984) 10–20.

    Google Scholar 

  7. W.J Paul. A 2.5n-lower bound on the combinational complexity of Boolean functions. SIAM J. comput. 6 (1977) 427–443.

    Google Scholar 

  8. A.K. Pulatov. Lower bounds on the complexity of implementation of characteristic functions of group codes by ∏-networks (in Russian). in Combinatorial-algebraic methods in applied mathematics, Gorki (1979) 81–95.

    Google Scholar 

  9. G.A. Tkachev. On the complexity of a sequence of Boolean functions by implementing in terms of circuits and ∏-circuits under additional restrictions on the circuits structure. ibid. (1980) 161–207.

    Google Scholar 

  10. L.G. Valiant. Exponential lower bounds for restricted monotone circuits. Proc. 15th ACM Symp. on Theory Comp. (1983).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kazan state university, 420008, Kazan, USSR

    R. G. Nigmatullin

Authors
  1. R. G. Nigmatullin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Lothar Budach

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nigmatullin, R.G. (1985). Are lower bounds on the complexity lower bounds for universal circuits?. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1985. Lecture Notes in Computer Science, vol 199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028817

Download citation

  • DOI: https://doi.org/10.1007/BFb0028817

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15689-5

  • Online ISBN: 978-3-540-39636-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation