Volume 22, No 5, 2015, P. 52-70
UDC 519.718.7
**Popkov K. A. **
Estimations on lengths of tests of functional elements under a large number of permissible faults
*Abstract:*
The problems of check of operability and state diagnosis of *N* logic gates which realize a given Boolean function *f* (*x*_{1}, … , *x*_{n}) in their perfect states are studied by means of composition of one-output logic circuits of them and observation of values produced by these circuits on any value sets of input variables. Random constant faults on outputs of gates are permitted; at the same time, it is assumed that not more than *k* gates are faulted, where *k* is a given natural number that does not rank over *N*. It is needed to minimize a number of circuits required for check of operability and determination of states of all gates. A lower bound on a number of these circuits is obtained when *k* is close to *N*. As a corollary from this bound it is derived that, under some condition for *N* and belonging of *k* to some segment, the number of circuits mentioned cannot be less than *ck*, where *c* > 1 is a constant which does not depend on choice of *k* from this segment.
Bibliogr. 15.
*Keywords:* logic gate, fault, logic circuit, check test, diagnostic test.
DOI: 10.17377/daio.2015.22.476
*Kirill A. Popkov *^{1}
1. Lomonosov Moscow State University
1 Leninskie Gory, 119991 Moscow, Russia
e-mail: kirill-formulist@mail.ru
Received 13 February 2015
Revised 22 July 2015
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