Multiplicative complexity of some Boolean functions
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Svetlana N. Selezneva
Abstract
The multiplicative (or conjunctive) complexity of a Boolean function f(x1, . . . , xn) (respectively, of a system of Boolean functions F = {f1, . . . , fm}) is the smallest number of AND gates in circuits in the basis {x&y, x ⊕ y, 1} implementing the function f (respectively, all the functions of system F). The multiplicative complexity of a function f (of a system of functions F) will be denoted by μ(f) (respectively, μ(F)). It will be shown that μ(f) = n − 1 if a function f(x1, . . . , xn) is representable as x1x2 . . . xn ⊕ q(x1, . . . , xn), where q is a function of degree two (n ≥ 3).Moreover,we show that μ(f) ≤ n−1 if a function f(x1, . . . , xn) is representable as a XOR sum of two multiaffine functions. Furthermore, μ(F) = n−1 if F = {x1x2 . . . xn , f(x1, . . . , xn)},where f is a function of degree two or a multiaffine function.
© 2015 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Weighing algorithms of classification and identification of situations
- Arithmetic complexity of the Stirling transforms
- Asymptotics of the logarithm of the number of (k, l)-sum-free sets in an Abelian group
- Multiplicative complexity of some Boolean functions
- On a statistic for testing the homogeneity of polynomial samples
Articles in the same Issue
- Frontmatter
- Weighing algorithms of classification and identification of situations
- Arithmetic complexity of the Stirling transforms
- Asymptotics of the logarithm of the number of (k, l)-sum-free sets in an Abelian group
- Multiplicative complexity of some Boolean functions
- On a statistic for testing the homogeneity of polynomial samples
