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Bounds on Shannon functions of lengths of contact closure tests for contact circuits. (English. Russian original) Zbl 1483.94079

Discrete Math. Appl. 31, No. 3, 165-178 (2021); translation from Diskretn. Mat. 32, No. 3, 49-67 (2020).
Summary: We consider the problem of synthesis of irredundant two-pole contact circuits which implement \(n\)-place Boolean functions and allow short single fault detection or diagnostic tests of closures of at most \(k\) contacts. We prove that the Shannon function of the length of a fault detection test is equal to \(n\) for any \(n\) and \(k\), and that the Shannon function of the length of a diagnostic test is majorized by \(n + k(n - 2)\) for \(n \geq 2\).

MSC:

94C11 Switching theory, applications of Boolean algebras to circuits and networks
94C12 Fault detection; testing in circuits and networks
94D10 Boolean functions
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