Related papers: Differentially 4-uniform functions
In this paper we define a new (output) multiplicative differential, and the corresponding $c$-differential uniformity. With this new concept, even for characteristic $2$, there are perfect $c$-nonlinear (PcN) functions. We first…
Rotation symmetric Boolean functions represent an interesting class of Boolean functions as they are relatively rare compared to general Boolean functions. At the same time, the functions in this class can have excellent properties, making…
Univariate specializations of Appell's hypergeometric functions F1, F2, F3, F4 satisfy ordinary Fuchsian equations of order at most 4. In special cases, these differential equations are of order 2, and could be simple (pullback)…
We present a top-down lower-bound method for depth-$4$ boolean circuits. In particular, we give a new proof of the well-known result that the parity function requires depth-$4$ circuits of size exponential in $n^{1/3}$. Our proof is an…
Evolving Boolean functions with specific properties is an interesting optimization problem since, depending on the combination of properties and Boolean function size, the problem can range from very simple to (almost) impossible to solve.…
We give the definition of uniform symmetric continuity for functions defined on a nonempty subset of the real line. Then we investigate the properties of uniformly symmetrically continuous functions and compare them with those of…
Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We…
We consider functions on the $d$-dimensional unit cube whose partial derivatives up to order $r$ are bounded by one. It is known that the minimal number of function values that is needed to approximate the integral of such functions up to…
In this paper we develop the idea of abstract homogeneity in the context of interval-valued (IV) functions endowed with admissible orders and investigate some of its properties.
Polymorphic circuits are a special kind of circuits which possess multiple build-in functions, and these functions are activated by environment parameters, like temperature, light and VDD. The behavior of a polymorphic circuit can be…
We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,'…
In this paper, we consider the characterization of the bentness of quadratic Boolean functions of the form $f(x)=\sum_{i=1}^{\frac{m}{2}-1} Tr^n_1(c_ix^{1+2^{ei}})+ Tr_1^{n/2}(c_{m/2}x^{1+2^{n/2}}) ,$ where $n=me$, $m$ is even and $c_i\in…
This paper is devoted to the construction of differential geometric invariants for the classification of "Quaternionic" vector bundles. Provided that the base space is a smooth manifold of dimension two or three endowed with an involution…
This paper introduces a novel quantum algorithm that is able to classify a hierarchy of classes of imbalanced Boolean functions. The fundamental characteristic of imbalanced Boolean functions is that the proportion of elements in their…
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…
Finding functions, particularly permutations, with good differential properties has received a lot of attention due to their varied applications. For instance, in combinatorial design theory, a correspondence of perfect $c$-nonlinear…
We determine all homogeneous metrics which are critical for some quadratic curvature functional in dimension four.
We show that the problem of counting the number of $n$-variable unate functions reduces to the problem of counting the number of $n$-variable monotone functions. Using recently obtained results on $n$-variable monotone functions, we obtain…
We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In…
We look at sections of a function bundle over the space of linear differential operators. We find that one can construct an isomorphism between a certain quotient bundle and the fourier counterpart of the original bundle defined by formal…