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Short Complete Fault Detection Tests for Logic Networks with Fan-In Two

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Abstract

It is established that we can implement almost every 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 at most 4 under arbitrary stuck-at faults at outputs of gates. The following assertions are also proved:We can implement each 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 at most one dummy variable and allowing a complete fault detection test of length at most 5 (at most 4, respectively) under faults of the same type.

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  1. Keldysh Institute of Applied Mathematics, Miusskaya pl. 4, Moscow, 125047, Russia

    K. A. Popkov

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  1. K. A. Popkov
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Russian Text © K.A. Popkov, 2019, published in Diskretnyi Analiz i Issledovanie Operatsii, 2019, Vol. 26, No. 1, pp. 89–113.

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Popkov, K.A. Short Complete Fault Detection Tests for Logic Networks with Fan-In Two. J. Appl. Ind. Math. 13, 118–131 (2019). https://doi.org/10.1134/S1990478919010137

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