Abstract
Maximal extensions of Post classes containing 0, 1, and x in the algebra of partially unreliable Boolean functions are described. Based on these extensions, criteria of expressibility of Boolean functions by circuits in a basis of partially unreliable elements are proved.
Similar content being viewed by others
References
Freivald, R.V., Functional Completeness for Nontotal Boolean Functions, in Diskretnyi analiz (Discrete Analysis), Novosibirsk: Inst. Mat. Sib. Otd. Akad. Nauk SSSR, 1966, issue 8, pp. 55–68.
Tarasov, V.V., A Test for the Completeness of Not Everywhere Defined Functions of the Algebra of Logic, Probl. Kibern., 1975, vol. 30, pp. 319–325.
Lozhkin, S.A., On the Synthesis of Formulas Using Not Everywhere Defined Functional Elements, in Proc. 6th Int. Conf. on Discrete Models in the Theory of Control Systems, Moscow, 2004, Moscow: Mosk. Gos. Univ., 2004, pp. 44–47.
Yablonskii, S.V., Gavrilov, G.P., and Kudryavtsev, V.B., Funktsii algebry logiki i klassy Posta (Boolean Functions and Post Classes), Moscow: Nauka, 1966.
Tarasov, V.V., On the Synthesis of Reliable Circuits from Unreliable Elements, Mat. Zametki, 1976, vol. 20, no. 3, pp. 391–400.
Author information
Authors and Affiliations
Additional information
Original Russian Text © V.V. Tarasov, 2006, published in Problemy Peredachi Informatsii, 2006, Vol. 42, No. 2, pp. 94–100.
Rights and permissions
About this article
Cite this article
Tarasov, V.V. To the problem of realizability of Boolean functions by circuits in a basis of unreliable functional elements. Probl Inf Transm 42, 152–157 (2006). https://doi.org/10.1134/S0032946006020086
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1134/S0032946006020086