RUS  ENG
Full version
JOURNALS // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika // Archive

Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2009 Number 5, Pages 55–57 (Mi vmumm905)

This article is cited in 3 papers

Short notes

Complexity of self-correcting circuits for some sequence of Boolean functions

V. M. Krasnov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: $k$-Self-correcting schemes of functional elements in the basis $\{x_1\& x_2,\bar x\}$ are considered. It is assumed that constant faults on outputs of functional elements are of the same type. Inverter are supposed to be reliable in service. The weight of each inverter is equal to $1$. Conjunctors can be reliable in service, or not reliable. Each reliable conjunctor implements a conjunction of two variables and has a weight $p>k+2$. Each unreliable conjunctor implements a conjunction in its correct state and implements a boolean constant $\delta$ ($\delta\in\{0,1\}$) otherwise. Each unreliable conjunctor has the weight 1. It is stated that the complexity of realization of monotone threshold symmetric functions $f_2^n(x_1,\dots,x_n)=\bigvee\limits_{\scriptscriptstyle 1\leq i < j \leq n}x_ix_j$, $n=3,4,\ldots$ by such schemes asymptotically equals $(k+3)n$.

Key words: schemes of the functional elements, complexity of implementation, Boolean functions.

UDC: 519.95

Received: 08.09.2008



Bibliographic databases:


© Steklov Math. Inst. of RAS, 2026