For functions of the algebra of logic in variables n, n = 1, 2, ..., asymptotically optimal in complexity from linear to dynamic activity of a circuit of functional elements in an arbitrary final complete basis B, in which among its functional elements, having the minimum reduced weight, or at least one of them implements FAL that has an isolated zero, and at least one implements a FAL that has isolated unit, or in the first (second) of the indicated cases an isolated zero (respectively, a unit) is a zero (respectively, a single) set.
Research into the possibility of building for "typical" and "most difficult" FAL of any implementing their CFE in a finite complete basis, which have asymptotically optimal complexity are characterized by a high level of protection against exposing functionality by hiding some local connections. Previously proposed methods for the synthesis of SFE in the standard basis are generalized to the case of an arbitrary nonsymmetric basis.
The report considers the lower and upper complexity estimates as called multicast multiplex operator in the class contact diagrams. The multicast multiplexer operator represents a system consisting of multiplexer functions, sets of address whose variables are different, and the sets of information variables match up. This operator allows you to access the same memory using several addresses at once.
In this paper, we show asymptotic upper and lower estimates for the complexity of the system of all Boolean functions (universal multipole) in the model of cellular circuits, having the form 2<sup>2<sup>n</sup>-1</sup>n(1 + O(1/n)).
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