Abstract
It is shown that the conjunction complexity L & k (f n2 ) of monotone symmetric Boolean functions \(f_2^n (x_1 , \ldots ,x_n ) = \mathop \vee \limits_{1 \leqslant i < j \leqslant n} x_i x_j\) realized by k-self-correcting circuits in the basis B = {&, −} asymptotically equals to (k + 2)n for growing n providing the price of a reliable conjunctor is ≥ k + 2.
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References
O. B. Lupanov, Asymptotic Estimates of Complexity of Control Circuits (Moscow State Univ., Moscow, 1984) [in Russian].
N. P. Red’kin, Discrete Mathematics (Fizmatlit, Moscow, 2009) [in Russian].
N. P. Red’kin, Reliability and Diagnostics of Circuits (Moscow State Univ., Moscow, 1992) [in Russian].
T. I. Krasnova, “Inversion Complexity of Self-Correcting Circuits for a Certain Sequence of Boolean Functions”, Vestn. Mosk. Univ. Matem., Mekhan., No. 3, 53 (2012) [Moscow Univ. Math. Bulletin 67 (3), 133 (2012)].
N. P. Red’kin, “Asymptotically Minimal Self-Correcting Schemes for a Sequence of Boolean Functions”, Diskret. Anal. Issled. Oper. 3(2), 62 (1996).
M. I. Grinchuk, “The Monotone Complexity of Threshold Functions”, in: Methods of Discrete Analysis in Graph Theory and Complexity Theory: Collected Papers, Vol. 52 (2) (Math. Inst. Sib. Branch of RAS, Novosibirsk, 1992), pp. 41–48.
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Original Russian Text © T.I. Krasnova, 2014, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2014, Vol. 69, No. 3, pp. 50–54.
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Krasnova, T.I. The conjunction complexity asymptotic of self-correcting circuits for monotone symmetric functions with threshold 2. Moscow Univ. Math. Bull. 69, 121–124 (2014). https://doi.org/10.3103/S0027132214030061
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DOI: https://doi.org/10.3103/S0027132214030061