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 Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, Number 5, Pages 47–50 (Mi vmumm268)

Short notes

Upper estimate of realization complexity of linear functions in a basis consisting of multi-input elements

Yu. A. Kombarov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The paper is devoted to realization of parity functions by circuits in the basis $U_\infty$. This basis contains all functions of form $(x_1^{\sigma_1}&\ldots& x_k^{\sigma_k})^{\beta}$. We present method of constructing circuts for pairity function of $n$ variables with complexity of $\lfloor (7n-4)/3\rfloor$. This improves previous known upper bound of $U_\infty$-complexity of parity function, that was $\lceil (5n-1)/2\rceil$. It is also shown that constructed circuits are minimal for very small $n$ (for $n<7$).

Key words: Boolean circuis, circuit complexity, parity function, minimal circuit.

 Funding Agency Grant Number Russian Foundation for Basic Research 14-01-00598

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English version:
Moscow University Mathematics Bulletin, 2015, 70:5, 226–229

Bibliographic databases:

UDC: 519.95

Citation: Yu. A. Kombarov, “Upper estimate of realization complexity of linear functions in a basis consisting of multi-input elements”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, no. 5, 47–50; Moscow University Mathematics Bulletin, 70:5 (2015), 226–229

Citation in format AMSBIB
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