Advertisement

On Networks Consisting of Functional Elements with Delays

  • O. B. Lupanov

Abstract

As is well known, in “traditional” methods for the realization of logic-algebra functions (by contact networks, II-networks, networks consisting of the functional elements, formulas) the so-called “Shannon effect” holds: “almost all functions” of n arguments have “an almost identical” complexity which is asymptotically equal to the complexity of the most complex function of n arguments. The hypothesis on this effect was stated by C. E. Shannon in 1949 (see [11]) and was subsequently proved by the author of the present paper (see, for example, [5, 3]). In certain cases (for example, for disjunctive normal forms) the “weakened Shannon effect” holds — “almost all functions of n arguments have almost identical complexity”; true, this complexity is less than the complexity of the most complex function [1, 7, 8].

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    V. V. Glagolev, “Some bounds for disjunctive normal forms of functions of the algebra of logic,” in: Systems Theory Research, Vol. 19, Consultants Bureau, New York (1970), p. 74.Google Scholar
  2. 2.
    V. B. Kudryavtsev, “Completeness theorem for a certain class of automata without feedbacks,” in: Problemy Kibernetiki, Vol. 8, Fizmatgiz, Moscow (1962), pp. 91–115.Google Scholar
  3. 3.
    O. B. Lupanov, “On the synthesis of certain classes of supervisory systems,” in: Problemy Kibernetiki, Vol. 10, Fizmatgiz, Moscow (1963), pp. 63–97.Google Scholar
  4. 4.
    O. B. Lupanov, “On a certain class of networks consisting of functional elements,” in: Problemy Kibernetiki, Vol. 7, Fizmatgiz, Moscow (1962), pp. 61–114.Google Scholar
  5. 5.
    O. B. Lupanov, “On a certain method of network synthesis,” Izvestiya Vuzov, Radiofizika, 1(1):120–140 (1958).Google Scholar
  6. 6.
    O. B. Lupanov, “On a certain approach to the synthesis of supervisory systems -the principle of local coding,” in: Problemy Kibernetiki, Vol. 14, Nauka, Moscow (1965), pp. 31–110.Google Scholar
  7. 7.
    S. V. Makarov, “The upper bound of the average length of a disjunctive normal form,” in: Discrete Analysis (Transactions of the Mathematics Institute, Siberian Branch, Academy of Sciences of the USSR), No. 3 (1964), pp. 78–80.Google Scholar
  8. 8.
    R. G. Nigmatullin, “The variational principle in logic algebra” in: Discrete Analysis (Transactions of the Mathematics Institute, Siberian Branch, Academy of Sciences of the USSR), No. 10 (1967), pp. 69–89.Google Scholar
  9. 9.
    S. V. Yablonskii, G. P. Gavrilov, and V. B. Kudryavtsev, Logic-Algebra Functions and Post Classes, Nauka, Moscow (1966).Google Scholar
  10. 10.
    E. L. Post, “Two-valued iterative systems in mathematical logic,” Princeton Ann. of Math. Studies, Vol. 5 (1941).Google Scholar
  11. 11.
    C. E. Shannon, “The synthesis of two-terminal switching circuits,” Bell System Technical Journal, 28(1):59–98 (1949).MathSciNetCrossRefGoogle Scholar

Copyright information

© Consultants Bureau, New York 1973

Authors and Affiliations

  • O. B. Lupanov
    • 1
  1. 1.MoscowRussia

Personalised recommendations