Video library: M. A. Alekhina, O. Yu. Barsukova, Asymptotically optimal in reliability curcuits in a basis consisting of the Webb function with the faults of type 0 at the outputs of gates

VIDEO LIBRARY


International workshop "Syntax and semantics of logical systems" August 11–16, 2019, Сamp site on the shore of Lake Hovsgol

Asymptotically optimal in reliability curcuits in a basis consisting of the Webb function with the faults of type 0 at the outputs of gates M. A. Alekhina^a, O. Yu. Barsukova^b ^a Penza State Technological University ^b Penza State University
Abstract: We consider the problem of the implementation of $k$-valued logics ($k \ge 3$) by circuits from unreliable gates in full basis consisting of the Webb function. We assume that gates of the circuit pass to fault states independently of each other, and they are exposed to single-type constant faults of type $0$ at the outputs. It is shown that with faults of type 0 almost any function of $k$-valued logics can be implemented by an asymptotically optimal in reliability circuit functioning with the unreliability which is asymptotically equal to unreliability of one basis element. The obtained result is valid in a dual (with respect to the permutation which is generated by the Lukashevich function) basis with single-type constant faults of type $k-1$ respectively.