Abstract. In this paper we find a lower bound of the second-order nonlinearities of Boolean bent functions of the form f(x) = Trn 1 (α1xd1 + α2xd2 ), where d1 and d2 are Niho ex...
We present a range of new results for testing properties of Boolean functions that are defined in terms of the Fourier spectrum. Broadly speaking, our results show that the propert...
Parikshit Gopalan, Ryan O'Donnell, Rocco A. Served...
We study the problem of testing isomorphism (equivalence up to relabelling of the variables) of two Boolean functions f, g : {0, 1}n → {0, 1}. Our main focus is on the most stud...
Recent work by Bernasconi, Damm and Shparlinski showed that the set of square-free numbers is not in AC0 , and raised as an open question whether similar (or stronger) lower bound...
In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3 − c lower bound ...