Boolean network models have gained popularity in computational systems biology over the last dozen years. Many of these networks use canalizing Boolean functions, which has led to increased interest in the study of these functions. The canalizing depth of a function describes how many canalizing variables can be recursively “picked off”, until a non-canalizing function remains. In this paper, w...

The square map is one of the functions that is used in cryptography. For instance, the square map is used in Rabin encryption scheme, block cipher RC6 and stream cipher Rabbit, in different forms. In this paper we study a special case of the square map, namely the square function modulo a power of two. We obtain probability distribution of the output of this map as a vectorial Boolean function....

We study the circuit complexity of boolean functions in a certain infinite basis. The basis consists of all functions that take value 1 on antichains over the boolean cube. We prove that the circuit complexity of the parity function and the majority function of n variables in this basis is b 2 c and ⌊ n 2 ⌋ +1 respectively. We show that the asymptotic of the maximum complexity of n-variable boo...

Although several methods for estimating the resistance of a random Boolean function against (fast) algebraic attacks were proposed, these methods are usually infeasible in practice for relative large input variables n (for instance n ≥ 30) due to increased computational complexity. An efficient estimation the resistance of Boolean function (with relative large input variables n) against (fast) ...

Threshold, 2-monotonic and interval Boolean functions constitute special classes of Boolean functions for which it is easy to decide many problems which are intractable for general Boolean functions. In our article we show that positive interval functions are a proper subset of positive threshold functions. Then we prove one property of 2-monotonic functions which is related to testing whether ...

In this paper was explored well known model k-OBDD. There are proven width based hierarchy of classes of boolean functions which computed by k-OBDD. The proof of hierarchy is based on sufficient condition of Boolean function’s non representation as k-OBDD and complexity properties of Boolean function SAF. This function is modification of known Pointer Jumping (PJ) and Indirect Storage Access (I...

In this paper was explored well known model k-OBDD. There are proven width based hierarchy of classes of boolean functions which computed by k-OBDD. The proof of hierarchy is based on sufficient condition of Boolean function’s non representation as k-OBDD and complexity properties of Boolean function SAF. This function is modification of known Pointer Jumping (PJ) and Indirect Storage Access (I...

Generalisations of the bent property of a boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic boolean functions are related to simple graphs and it is shown that the orbit generated by successive Local Complementations on a graph can be found within the transform spectra under investigation. The flat spectra of ...