High-accuracy asymptotic bounds for the realization complexity of function systems by iterative contact circuits

Abstract

We investigate the realization complexity of systems of Boolean functions in the class of iterative contact circuits -an extension of the class of contact circuits. The objective is to obtain so-called high-accuracy asymptotic bounds for the Shannon function L ICC (n, m), which describe the asymptotic behavior of both the Shannon function and the first residual term in its asymptotic expansion. We show that for m < 2 2 (n−1)/2 −n we have the bound L ICC (n, m) = m · 2 n−1 n + log m " 1 + 5 log(n + log m) 2(n + log m)The problem is thus solved with a fairly weak constraint on the number of functions.

Single fault detection tests for generalized iterative switching circuits

“…Note that the difference between the GISCs and the iterative switching circuits (ISCs) is that all switches attached in the ISCs to control variable outputs must normally be off (i.e., without negation). Accurate asymptotic estimates were obtained in [5] for the Shannon function of the complexity of realiz ing function systems with the help of ISCs.…”