Abstract
We investigate the possibility of obtaining a function which depends essentially on an arbitrary number of arguments from the functions of some finite system in Pk. We introduce a characteristic of the initial finite system, by means of which we express the complexity of obtaining the simplest function of the given number of variables. The estimate obtained below, for the Shannon function for the realization of functions in Pk by formulas, is higher than the one known earlier.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
S. V. Yablonskii, “Functional constructions in k-valued logic,” Tr. Matem. In-ta AN SSSR,51, 5–142 (1958).
O. B. Lupanov, “On the complexity of the realization of the functions of an algebra of logic by formulas,” in: Problemy Kibernetiki, No. 3, Moscow (1960), pp. 61–80.
O. B. Lupanov, “On the synthesis of certain classes of control systems,” in: Problemy Kibernetiki, No. 10, Moscow (1963), pp. 63–97.
R. E. Krichevskii, “On the realization of functions by superpositions,” in: Problemy Kibernetiki, No. 2, Moscow (1960), pp. 123–138.
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki. Vol. 12, No. 1, pp. 3–12, July, 1972.
Rights and permissions
About this article
Cite this article
Zakharova, E.Y., Yablonskii, S.V. Certain properties of nondegenerate superpositions in Pk . Mathematical Notes of the Academy of Sciences of the USSR 12, 435–440 (1972). https://doi.org/10.1007/BF01094386
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01094386