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

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, xy, x ~ y} (in the basis {xy, xy, 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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Correspondence to N. E. Aleksandrova.

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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