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Short single tests for circuits with arbitrary stuck-at faults at outputs of gates

  • Kirill A. Popkov EMAIL logo
Published/Copyright: October 20, 2019

Abstract

The following results are proved:

  1. any nonconstant Boolean function may be implemented by an irredundant circuit of gates in the basis {x& y, x, xyz} admitting a single fault detection test of length at most 2 with respect to arbitrary stuck-at faults at outputs of gates,

  2. there exists a six-place Boolean function ψ such that any nonconstant Boolean function may be implemented by an irredundant circuit of gates in the basis {ψ} admitting a single diagnostic test of length at most 3 with respect to arbitrary stuck-at faults at outputs of gates.


Funding

This research was carried out with the financial support of the Russian Science Foundation (RSF) grant 14-21-00025 P.

Originally published in Diskretnaya Matematika (2018) 30, №3, 99–116 (in Russian).


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Received: 2017-06-26
Published Online: 2019-10-20
Published in Print: 2019-10-25

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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