This article is cited in 2 papers

A lower bound for the complexity of generalized parallel-serial contact circuits for a characteristic function of divisibility by $q$

K. L. Rychkov

S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia

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.

UDC: 519.714

Received: 26.06.2010

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