On the design of switching circuits admitting small detection test sets

Abstract

It is established that, for an arbitrary nonconstant Boolean function f(x ₁,..., x _n ), there exist the following testable switching circuits that admit a single fault detection test set of cardinality O(n): (a) a three-pole switching circuit (with one input and two output poles) that realizes a system of functions (f, $\bar f$) and (b) a two-pole switching circuit that realizes a function f(x ₁,..., x _n ) ⊕ x _n +1. It is also proved that almost all Boolean functions f(x ₁,..., x _n ) can be realized by two-pole switching circuits that admit small detection test sets (test sets of cardinality O(n)) under homogeneous faults of switches (closures or breakings).