Volume 17, No 6, 2010, P. 68-76

UDC 519.714
K. L. Rychkov
A lower bound for the complexity of generalized parallel-serial contact circuits for a characteristic function of divisibility by q

Abstract:
We consider generalization of the concept of a parallel-serial contact circuit in the case when the variables assigned to contacts can take not two as in the Boolean case but a greater number of values. The conductivity of contacts as well as in the Boolean case remains two-valued (a contact is either close or break). We obtain a lower bound for the complexity of such circuits computing the characteristic function of divisibility by $q$, i.e., the function $\varphi_q\colon\{0,1,\dots,q-1\}^n\to\{0,1\}$ which is equal to 1 if the sum of values of its variables is divided by $q$.
Bibliogr. 6.

Keywords: Boolean function, contact circuit, complexity of circuits.

Rychkov Konstantin Leonidovich ¹
1. S. L. Sobolev Institute of Mathematics, SB RAS,
4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
e-mail: rychkov@math.nsc.ru