On Networks Consisting of Functional Elements with Delays

O. B. Lupanov

A chapter in Systems Theory Research, 1973, pp 43-83 from Springer

Abstract: 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].

Date: 1973
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DOI: 10.1007/978-1-4757-0079-4_3

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