Abstract
Realization of functions of the k-valued logic by circuits is considered over an arbitrary finite complete basis B. Asymptotic behavior of the Shannon function D B (n) of the circuit depth over B is examined. 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 natural k ≥ 2 and for any finite complete basis B there exists a positive constant α B such that D B (n) ∼ α B n for n → ∞.
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References
O. B. Lupanov, “Circuits of Functional Elements with Delay,” Problemy Kibern. 23, 43 (1970).
G. Pólya and G. Szegö, Problems and Theorems in Analysis. I (Springer-Verlag, N.Y., 1978; Nauka, Moscow, 1978).
O. B. Lupanov, “Synthesis of Some Classes of Control Systems,” Problemy Kibern. 10, 64 (1963).
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Original Russian Text © A.V. Kochergin, 2013, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2013, Vol. 68, No. 1, pp. 56–59.
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Kochergin, A.V. Depth of functions of k-valued logic in finite bases. Moscow Univ. Math. Bull. 68, 77–79 (2013). https://doi.org/10.3103/S0027132213010178
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DOI: https://doi.org/10.3103/S0027132213010178