We prove that, for n≥2, one can implement each Boolean function on n variables by a two-pole contact circuit which is irredundant and allows a diagnostic test with a length not exceeding n+k(n-2) under not more than k contact breaks. We obtain that, under k=k(n) ≤2^n-4, for almost all Boolean functions on n variables, the least possible length of such a test does not exceed 2k+2.

contact circuit, contact break, diagnostic test

Mathematical modelling in actual problems of science and technics

Popkov Kirill Andreevich,  ,  orcid.org/0000-0003-3763-4050,  KIAM RAS