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

Preliminary version
  • R. G. Nigmatullin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 199)


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. Blum. A Boolean function requiring 3n network size. Theor. Comp. Sci. 28 (1984) 337–345.Google Scholar
  2. 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. 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. 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. 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. 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. 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. 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. 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. 10.
    L.G. Valiant. Exponential lower bounds for restricted monotone circuits. Proc. 15th ACM Symp. on Theory Comp. (1983).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • R. G. Nigmatullin
    • 1
  1. 1.Kazan state universityKazanUSSR

Personalised recommendations