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Tests of contact closure for contact circuits

  • Kirill A. Popkov EMAIL logo
Published/Copyright: November 8, 2016
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Discrete Mathematics and Applications
From the journal Discrete Mathematics and Applications Volume 26 Issue 5

Abstract

The paper is concerned with the problem of synthesis of two-pole contact circuits implementing n-place Boolean functions and admitting short fault detection and diagnostic tests with respect to closures of contacts. It is shown that almost all n-place Boolean functions are implemented by irredundant two-pole contact circuits admitting single fault detection, complete fault detection and single diagnostic tests of constant length. We also prove that: 1) any Boolean function f(x1,...,xn) may be implemented by an irredundant two-pole contact circuit containing at most one input variable distinct from the variables x1,...,xn and admitting single and complete fault detection tests of length at most 2n; 2) any Boolean function f(x1,...,xn) may be implemented by an irredundant two-pole contact circuit containing at most two input variables distinct from the variables x1,...,xn and admitting single diagnostic test of length at most 4n.

keywords: contact circuit; contact closure; fault detection test; diagnostic test

Originally published in Diskretnaya Matematika (2016) 28, №1, 87–100 (in Russian).

Funding source: Russian Foundation for Basic Research

Award Identifier / Grant number: 14-01-00598

Funding statement: The author was supported by the Russian Foundation for Basic Research (project no. 14-01-00598) and the Program of Basic Research of the Mathematical Science Division of the Russian Academy of Sciences “Algebraic and Combinatorial Methods of Mathematical Cybernetics and Information Systems of New Generation” (project “The Problems of Optimal Synthesis of Control Systems”)

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Received: 2015-7-28
Published Online: 2016-11-8
Published in Print: 2016-10-1

© 2016 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Research Article
  3. A generalization of Ore’s theorem on polynomials
  4. Research Article
  5. The sum of modules of Walsh coefficients of Boolean functions
  6. Research Article
  7. The algorithm for identical object searching with bounded worst-case complexity and linear memory
  8. Research Article
  9. Tests of contact closure for contact circuits
  10. Research Article
  11. Orbital derivatives over subgroups and their combinatorial and group-theoretic properties
https://doi.org/10.1515/dma-2016-0025
Keywords for this article
contact circuit; contact closure; fault detection test; diagnostic test

Articles in the same Issue

  1. Frontmatter
  2. Research Article
  3. A generalization of Ore’s theorem on polynomials
  4. Research Article
  5. The sum of modules of Walsh coefficients of Boolean functions
  6. Research Article
  7. The algorithm for identical object searching with bounded worst-case complexity and linear memory
  8. Research Article
  9. Tests of contact closure for contact circuits
  10. Research Article
  11. Orbital derivatives over subgroups and their combinatorial and group-theoretic properties
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