Tests of contact closure for contact circuits
Кирилл Андреевич Попков · Discrete Mathematics and Applications · 2016
Abstract The paper is concerned with the problem of synthesis of two-pole contact circuits implementing n -place Boolean functions and admitting short fault detection and diagnostic tests with respect to closures of contacts. It is shown that almost all n -place Boolean functions are implemented by irredundant two-pole contact circuits admitting single fault detection, complete fault detection and single diagnostic tests of constant length. We also prove that: 1) any Boolean function f ( x 1 ,..., x n ) may be implemented by an irredundant two-pole contact circuit containing at most one input variable distinct from the variables x 1 ,..., x n and admitting single and complete fault detection tests of length at most 2 n ; 2) any Boolean function f ( x 1 ,..., x n ) may be implemented by an irredundant two-pole contact circuit containing at most two input variables distinct from the variables x 1 ,..., x n and admitting single diagnostic test of length at most 4 n .