Related papers: Pairing Functions, Boolean Evaluation and Binary D…
Early in 1992, Deutsch-Jozsa algorithm computed a symmetric partial Boolean function with a single quantum query, and thus achieved the best separation between classical deterministic and exact quantum query complexity. Until recent years,…
In this review we present hyper-dual numbers as a tool for the automatic differentiation of computer programs via operator overloading. We start with a motivational introduction into the ideas of algorithmic differentiation. Then we…
We present a simple and consistent way to compute correlation functions in interacting theories with non-trivial phase diagram. As an example we show how to consistently compute the four-point function in three dimensional…
Encodings, that is, injective functions from words to words, have been studied extensively in several settings. In computability theory the notion of encoding is crucial for defining computability on arbitrary domains, as well as for…
Items in a test are often used as a basis for making decisions and such tests are therefore required to have good psychometric properties, like unidimensionality. In many cases the sum score is used in combination with a threshold to decide…
A certain analysis of all possible associative binary operations on N is presented. This is equivalent with an analysis of all possible monoid structures on N. Several results and a conjecture in this regard are given.
We examine several aspects of explicability of a classification system built from neural networks. The first aspect is the pairwise explicability, which is the ability to provide the most accurate prediction when the range of possibilities…
The aim of this paper is to prove that every polynomial function that maps the natural integers to the positive integers is the growth function of some D0L-system.
The goal in the area of functions property testing is to determine whether a given black-box Boolean function has a particular given property or is $\varepsilon$-far from having that property. We investigate here several types of properties…
Statistical matching is an effective method for estimating causal effects in which treated units are paired with control units with ``similar'' values of confounding covariates prior to performing estimation. In this way, matching helps…
A Boolean network (BN) with $n$ components is a discrete dynamical system described by the successive iterations of a function $f:\{0,1\}^n \to \{0,1\}^n$. This model finds applications in biology, where fixed points play a central role.…
In real-world data, information is stored in extremely large feature vectors. These variables are typically correlated due to complex interactions involving many features simultaneously. Such correlations qualitatively correspond to…
In the context of knowledge compilation (KC), we study the effect of augmenting Ordered Binary Decision Diagrams (OBDD) with two kinds of decomposition nodes, i.e., AND-vertices and OR-vertices which denote conjunctive and disjunctive…
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
A fuzzy Boolean function is a map $f:\cube^n\to [0,1]$, where $n\in\mathbb N$. We introduce and compare three ways of saying that such a function has bounded complexity. The first is a sampling property: the value $f(x)$ can be recovered,…
Function-correcting codes are a class of codes designed to protect the function evaluation of a message against errors whose key advantage is the reduced redundancy. In this paper, we extend function-correcting codes from binary symmetric…
The polylogarithm function is one of the constellation of important mathematical functions. It has a long history, and many connections to other special functions and series, and many applications, for instance in statistical physics.…
We will study some important properties of Boolean functions based on newly introduced concepts called Special Decomposition of a Set and Special Covering of a Set. These concepts enable us to study important problems concerning Boolean…
In this paper, we give a new approach for the study of Weyl-type theorems. Precisely we introduce the concepts of spectral valued and spectral partitioning functions. Using two natural order relations on the set of spectral valued…
We use a labelled deduction system based on the concept of computational paths (sequences of rewrites) as equalities between two terms of the same type. We also define a term rewriting system that is used to make computations between these…