Regular symmetric groups of boolean functions

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...

Relationships between Boolean Functions and Symmetric Groups

We study the relations between boolean functions and symmetric groups. We consider elements of a symmetric group as variable transformation operators for boolean functions. Boolean function may be xed or permuted by these operators. We give some properties relating the symmetric group Sn and boolean functions on Vn.

Symmetry groups of boolean functions

We prove that every abelian permutation group, but known exceptions, is the symmetry group of a boolean function. This solves the problem posed in the book by Clote and Kranakis. In fact, our result is proved for a larger class of groups, namely, for all groups contained in direct sums of regular groups. We investigate the problem of representability of permutation groups by the symmetry groups...

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...

Stochastic Evaluation of Symmetric Boolean Functions