Volume 22, No 5, 2015, P. 52-70
Popkov K. A.
Estimations on lengths of tests of functional elements under a large number of permissible faults
The problems of check of operability and state diagnosis of N logic gates which realize a given Boolean function f (x1, … , xn) 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.
Keywords: logic gate, fault, logic circuit, check test, diagnostic test.
Kirill A. Popkov 1
1. Lomonosov Moscow State University
1 Leninskie Gory, 119991 Moscow, Russia
Received 13 February 2015
Revised 22 July 2015
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