Abstract
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 ⩾ 2.
Originally published in Diskretnaya Matematika (2020) 32,№3, 49–67 (in Russian).
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- On the action of the implicative closure operator on the set of partial functions of the multivalued logic
- Bounds on Shannon functions of lengths of contact closure tests for contact circuits
- Conditions of A-completeness for linear automata over dyadic rationals
- Learning of monotone functions with single error correction
- Multitype weakly subcritical branching processes in random environment
- Convex algebras of probability distributions induced by finite associative rings
Articles in the same Issue
- Frontmatter
- On the action of the implicative closure operator on the set of partial functions of the multivalued logic
- Bounds on Shannon functions of lengths of contact closure tests for contact circuits
- Conditions of A-completeness for linear automata over dyadic rationals
- Learning of monotone functions with single error correction
- Multitype weakly subcritical branching processes in random environment
- Convex algebras of probability distributions induced by finite associative rings