Related papers: A Search for Nonlinear Balanced Boolean Functions …
Idempotent Boolean functions form a highly structured subclass of Boolean functions that is closely related to rotation symmetry under a normal-basis representation and to invariance under a fixed linear map in a polynomial basis. These…
A Boolean function of n bits is balanced if it takes the value 1 with probability 1/2. We exhibit a balanced Boolean function with a randomized evaluation procedure (with probability 0 of making a mistake) so that on uniformly random…
Local search is widely used to solve combinatorial optimisation problems and to model biological evolution, but the performance of local search algorithms on different kinds of fitness landscapes is poorly understood. Here we consider how…
An algorithm for computing the nonlinearity of a Boolean function from its algebraic normal form (ANF) is proposed. By generalizing the expression of the weight of a Boolean function in terms of its ANF coefficients, a formulation of the…
Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between…
First, we construct a class of functions with good local avalanche characteristics, but bad global avalanche characteristics. We also derive some bounds for the nonlinearity of such functions. It improves upon the results of Son et al., and…
We examine a hierarchy of equivalence classes of quasi-random properties of Boolean Functions. In particular, we prove an equivalence between a number of properties including balanced influences, spectral discrepancy, local strong…
This paper presents a method to detect and recognize symmetries in Boolean functions. The idea is to use information theoretic measures of Boolean functions to detect sub-space of possible symmetric variables. Coupled with the new…
The use of balanced crossover operators in Genetic Algorithms (GA) ensures that the binary strings generated as offsprings have the same Hamming weight of the parents, a constraint which is sought in certain discrete optimization problems.…
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…
Feature selection problems have been extensively studied for linear estimation, for instance, Lasso, but less emphasis has been placed on feature selection for non-linear functions. In this study, we propose a method for feature selection…
Advances in neural architecture search, as well as explainability and interpretability of connectionist architectures, have been reported in the recent literature. However, our understanding of how to design Bayesian Deep Learning (BDL)…
We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and…
We address the problem of finding optimal strategies for computing Boolean symmetric functions. We consider a collocated network, where each node's transmissions can be heard by every other node. Each node has a Boolean measurement and we…
Whereas the design and properties of bent and plateaued functions have been frequently addressed during the past few decades, there are only a few design methods of so-called 5-valued spectra Boolean functions whose Walsh spectra takes the…
The study of non-linearity (linearity) of Boolean function was initiated by Rothaus in 1976. The classical non-linearity of a Boolean function is the minimum Hamming distance of its truth table to that of affine functions. In this note we…
We consider collocated wireless sensor networks, where each node has a Boolean measurement and the goal is to compute a given Boolean function of these measurements. We first consider the worst case setting and study optimal block…
The advent of highly accurate protein structure prediction methods has fueled an exponential expansion of the protein structure database. Consequently, there is a rising demand for rapid and precise structural homolog search. Traditional…
The vectorial Boolean functions are employed in cryptography to build block coding algorithms. An important criterion on these functions is their resistance to the differential cryptanalysis. Nyberg defined the notion of almost perfect…
In this paper, we develop upon the topic of loss function learning, an emergent meta-learning paradigm that aims to learn loss functions that significantly improve the performance of the models trained under them. Specifically, we propose a…