We consider a problem of synthesis of two-pole contact circuits which realize Boolean functions on n variables and permit of short fault detection and diagnostic tests regarding contact closures. It is obtained than almost all Boolean functions on n variables are realizable by irredundant two-pole contact circuits which permit of single fault detection, complete fault detection, and single diagnostic tests of a constant length. The following facts are also proved:
1) each Boolean function f(x1,…,xn) can be realized by an irredundant two-pole contact circuit which contains not more than one input variable different from variables x1,…,xn and permits of single and complete fault detection tests lengths of which do not exceed 2n;
2) each Boolean function f(x1,…,xn) can be realized by an irredundant two-pole contact circuit which contains not more than two input variables different from variables x1,…,xn and permits of a single diagnostic test a length of which does not exceed 4n.
contact circuit, contact closure, single fault detection test, complete fault detection test, single diagnostic test
Mathematical modelling in actual problems of science and technics