Abstract
The realization of functions of the k-valued logic by circuits is considered over an arbitrary infinite complete basis B. The Shannon function D B (n) of the circuit depth over B is examined (for any positive integer n the value D B (n) is the minimal depth sufficient to realize every function of the k-valued logic of n variables by a circuit over B). It is shown that for each fixed k ≥ 2 and for any infinite complete basis B either there exists a constant α ≥ 1 such that D B (n) = α for all sufficiently large n, or there exist constants β (β > 0), γ, δ such that βlog2 n ≤ D B (n) ≤ γlog2 n + δ for all n.
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Original Russian Text © A.V. Kochergin, 2011, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2011, Vol. 66, No. 1, pp. 22–26.
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Kochergin, A.V. Depth of functions of the k-valued logic in infinite bases. Moscow Univ. Math. Bull. 66, 20–24 (2011). https://doi.org/10.3103/S0027132211010049
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DOI: https://doi.org/10.3103/S0027132211010049