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Diagnostic tests for local coalescences of variables in Boolean functions

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The article studies diagnostic tests for local k -fold coalescences of variables in Boolean functions \( f\left( {{{\tilde{x}}^n}} \right)\left( {1 \leq k \leq n,\;1 \leq t \leq {2^{{2^k}}}} \right) \). Upper and lower bounds are proved for the Shannon function of the length of the diagnostic test for local k -fold coalescences generated by the system of functions \( \Phi_t^k \). The Shannon function of the length of a complete diagnostic test for local k -fold coalescences behaves asymptotically as 2k (n − k + 1) for n → ∞, k → ∞.

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

    D. S. Romanov

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  1. D. S. Romanov
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Correspondence to D. S. Romanov.

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Translated from Prikladnaya Matematika i Informatika, No. 36, pp. 91–98, 2010.

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Romanov, D.S. Diagnostic tests for local coalescences of variables in Boolean functions. Comput Math Model 23, 72–78 (2012). https://doi.org/10.1007/s10598-012-9119-0

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  • DOI: https://doi.org/10.1007/s10598-012-9119-0

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