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Journal of Applied and Industrial Mathematics, 2019, 13:1, 118-131

Volume 26, No 1, 2019, P. 89-113

UDC 519.718.7
K. A. Popkov
Short complete fault detection tests for logic networks with fan-in two

Abstract:
It is established that we can implement almost every Boolean function on $n$ variables by a logic network in the basis {$x \And y, x \lor y, x \oplus y, 1$}, 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 {$x \And y, x \lor y, x \oplus y, 1$} (in the basis {$x \And y, x \lor y, x \lor \bar{y}, x \oplus y$}) 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.
Illustr. 2, bibliogr. 24.

Keywords: logic network, arbitrary stuck-at fault, complete fault detection test.

DOI: 10.33048/daio.2019.26.623

Kirill A. Popkov 1
1. Keldysh Institute of Applied Mathematics,
4 Miusskaya Square, 125047 Moscow, Russia
e-mail: kirill-formulist@mail.ru

Received July 16, 2018
Revised August 2, 2018
Accepted November 28, 2018

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