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On the multiplicative complexity of some Boolean functions

  • S. N. SeleznevaEmail author
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Abstract

In this paper, we study the multiplicative complexity of Boolean functions. The multiplicative complexity of a Boolean function f is the smallest number of &-gates in circuits in the basis {x & y, xy, 1} such that each such circuit computes the function f. We consider Boolean functions which are represented in the form x 1, x 2x n q(x 1, ⋯, x n ), where the degree of the function q(x 1, ⋯, x n ) is 2. We prove that the multiplicative complexity of each such function is equal to (n − 1). We also prove that the multiplicative complexity of Boolean functions which are represented in the form x 1x n r(x 1, ⋯, x n ), where r(x 1, ⋯, x n ) is a multi-affine function, is, in some cases, equal to (n − 1).

Keywords

Boolean function circuit complexity multiplicative complexity upper bound 

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia

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