The conjunction complexity asymptotic of self-correcting circuits for monotone symmetric functions with threshold 2

Abstract

It is shown that the conjunction complexity Lk&(f2n) of monotone symmetric Boolean functions \(f_2^n (x_1 , \ldots ,x_n ) = \mathop \vee \limits_{1 \leqslant i < j \leqslant n} x_i x_j\) realized by k-self-correcting circuits in the basis B = {&, −} asymptotically equals to (k + 2)n for growing n providing the price of a reliable conjunctor is ≥ k + 2.