Symmetric Boolean Functions

Generalized Rotation Symmetric and Dihedral Symmetric Boolean Functions - 9 Variable Boolean Functions with Nonlinearity 242

Recently, 9-variable Boolean functions having nonlinearity 241, which is strictly greater than the bent concatenation bound of 240, have been discovered in the class of Rotation Symmetric Boolean Functions (RSBFs) by Kavut, Maitra and Yücel. In this paper, we present several 9-variable Boolean functions having nonlinearity of 242, which we obtain by suitably generalizing the classes of RSBFs an...

Regular symmetric groups of boolean functions

is called a Boolean function. By Aut(f) we denote the set of all symmetries of f , i.e., these permutation σ ∈ Sn for which f(xσ(1), . . . , xσ(n)) = f(x1, . . . , xn). We show the solution of a problem posed by A. Kisielewicz ([1]). We show that, with the exception of four known groups of small order, every regular permutation group is isomorphic with Aut(f) for some Boolean function f . We pr...

Stochastic Evaluation of Symmetric Boolean Functions

On the Balanced Elementary Symmetric Boolean Functions

or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. SUMMARY In this paper, we give some results towards the conject...

Quadratization of Symmetric Pseudo-Boolean Functions

A pseudo-Boolean function is a real-valued function f(x) = f(x1, x2, . . . , xn) of n binary variables; that is, a mapping from {0, 1}n to R. For a pseudo-Boolean function f(x) on {0, 1}n, we say that g(x, y) is a quadratization of f if g(x, y) is a quadratic polynomial depending on x and on m auxiliary binary variables y1, y2, . . . , ym such that f(x) = min{g(x, y) : y ∈ {0, 1}m} for all x ∈ ...