There are two construction methods of designs from $(n,m)$ -bent functions, known as translation and addition designs. In this article we analyze, which equivalence relation for Boolean bent i.e. notation="LaTeX">$(n,1)$ vectorial fun...

In this paper we generate upper and lower bounds for the sensitivity to noise of a Boolean function using relaxed assumptions on input choices and noise. The robustness of a Boolean network to noisy inputs is related to the average sensitivity of that function. The average sensitivity measures how sensitive to changes in the inputs the output of the function is. The average sensitivity of Boole...

This paper studies the robust stabilization of impulsive Boolean control networks (IBCNs) with function perturbation. A network (BCN) a state-dependent sequence is converted to an equivalent BCN by semi-tensor product method. Based on equivalence between IBCN and corresponding BCN, several criteria are proposed for IBCNs. Furthermore, when not robustly stabilizable after perturbation, algorithm...

Recently, balanced 15-variable Boolean functions with nonlinearity 16266 were obtained by suitably modifying unbalanced Patterson-Wiedemann (PW) functions, which possess nonlinearity 2–2 + 20 = 16276. In this short paper, we present an idempotent (interpreted as rotation symmetric Boolean function) with nonlinearity 16268 having 15 many zeroes in the Walsh spectrum, within the neighborhood of P...

We investigate the influences of variables on a Boolean function f based on the quantum BernsteinVazirani algorithm. A previous paper has proved that if a n-variable Boolean function f(x1, · · · , xn) does not depend on an input variable xi, using the Bernstein-Vazirani circuit to f will always obtain an output y that has a 0 in the ith position. We generalize this result and show that after se...

Boolean reversible circuits are boolean circuits made of reversible elementary gates. Despite their constrained form, they can simulate any boolean function. The synthesis and validation of a reversible circuit simulating a given function is a difficult problem. In 1973, Bennett proposed to generate reversible circuits from traces of execution of Turing machines. In this paper, we propose a nov...