A method of synthesis of irredundant circuits admitting single fault detection tests of constant length
Дмитрий Сергеевич Романов, E. Yu. Romanova · Discrete Mathematics and Applications · 2019
Abstract A constructive proof is given that in each of the bases B ′ = { x & y , x ⊕ y , x ∼ y }, B 1 = { x & y , x ⊕ y , 1} any n -place Boolean function may be implemented: by an irredundant combinational circuit with n inputs and one output admitting (under single stuck-at faults at inputs and outputs of gates) a single fault detection test of length at most 16, by an irredundant combinational circuit with n inputs and one output admitting (under single stuck-at faults at inputs and outputs of gates and at primary inputs) a single fault detection test of length at most 2 n −2log 2 n + O (1); besides, there exists an n -place function that cannot be implemented by an irredundant circuit admitting a detecting test whose length is smaller than 2 n −2log 2 n − Ω (1), by an irredundant combinational circuit with n inputs and three outputs admitting (under single stuck-at faults at inputs and outputs of gates and at primary inputs) a single fault detection test of length at most 17.