The Length of a Single Fault Detection Test for Constant-Nonpreserving Element Insertions

Computational Mathematics and Modeling volume 31, pages484–493(2020)Cite this article

We prove that every Boolean function other than the constant and the identity function can be realized by an irredundant combinational circuit in the basis {xy, x ⊕ y, x ~ y} (in the basis {x ∨ y, x ⊕ y, x ~ y}) that admits a single detection test of length 1 with respect to element insertions not preserving the same constant.

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Author information

Affiliations

  1. GlowByte Consulting, Moscow, Russia

    N. E. Aleksandrova

  2. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia

    D. S. Romanov

Authors
  1. N. E. Aleksandrova
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  2. D. S. Romanov
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Correspondence to N. E. Aleksandrova.

Additional information

Translated from Prikladnaya Matematika i Informatika, No. 64, 2020, pp. 64–78.

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Aleksandrova, N.E., Romanov, D.S. The Length of a Single Fault Detection Test for Constant-Nonpreserving Element Insertions. Comput Math Model 31, 484–493 (2020). https://doi.org/10.1007/s10598-021-09510-5

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Keywords

  • combinational circuits
  • detection test
  • element insertion
  • Shannon function of test length