Abstract
Abstract A constructive proof is given that in each of the bases B′ = {x&y, x⊕y, x ∼ y}, B1 = {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 2n−2log2 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 2n−2log2 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.
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