EN|RU Volume 16, No 6, 2009, P. 12-22 UDC 519.718 A. V. Vasin Synthesis of asymptotically optimal reliable circuits in basis $\{\&,\lnot\}$ Abstract: Circuits of unreliable functional elements are considered in the basis $\{\&,\lnot\}$. It is possible to realize almost all boolean functions by asymptotically optimal reliable circuits. Unreliability of these circuits is asymptotically equal to $5\varepsilon$ for almost all Boolean functions with $\varepsilon\to0$ ($\varepsilon$ is the probability of inverse failure at the output of the base element). Ill. 5, bibl. 4. Keywords: synthesis of circuits, unreliable element, inverse failure, asymptotically optimal reliable circuits. Vasin Aleksei Valer’evich 1 1. Penza State University, 40 Krasnaya str., 440017 Penza, Russia e-mail: alvarvasin@mail.ru © Sobolev Institute of Mathematics, 2015