It is established that one can implement almost any Boolean function on n variables by a logic network in the basis {x&y,x∨y,x⊕y,1}, allowing a complete fault detection test with length not exceeding 4 under arbitrary stuck-at faults at outputs of gates. The following assertions are also proved: one can implement any Boolean function on n variables by a logic network in the basis {x&y,x∨y,x⊕y,1} (in the basis {x&y,x∨y,x∨y¯,x⊕y}), containing not more than one dummy variable and allowing a complete fault detection test with length not exceeding 5 (not exceeding 4, respectively) under faults of the same type.

logic network, arbitrary stuck-at fault, complete fault detection test

Mathematical modelling in actual problems of science and technics

Popkov Kirill Andreevich,  kirill-formulist@mail.ru,  orcid.org/0000-0003-3763-4050,  KIAM RAS