On Networks Consisting of Functional Elements with Delays
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 ) 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].
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- 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.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.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.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.O. B. Lupanov, “On a certain method of network synthesis,” Izvestiya Vuzov, Radiofizika, 1(1):120–140 (1958).Google Scholar
- 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.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.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.S. V. Yablonskii, G. P. Gavrilov, and V. B. Kudryavtsev, Logic-Algebra Functions and Post Classes, Nauka, Moscow (1966).Google Scholar
- 10.E. L. Post, “Two-valued iterative systems in mathematical logic,” Princeton Ann. of Math. Studies, Vol. 5 (1941).Google Scholar