Related papers: On the complexity of finite valued functions
Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…
We study testing properties of functions on finite groups. First we consider functions of the form $f:G \to \mathbb{C}$, where $G$ is a finite group. We show that conjugate invariance, homomorphism, and the property of being proportional to…
Differential equations where the graph of some derivative of a function is composed of a finite number of similarity transformations of the graph of the function itself are defined. We call these self-similar differential equations (SSDEs)…
Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a knowledge representation that is useful in mechanizing decision theoretic planning in relational domains. GFODDs generalize function-free first order logic and…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
We consider approximation problems for a special space of d variate functions. We show that the problems have small number of active variables, as it has been postulated in the past using concentration of measure arguments. We also show…
A deep approximation is an approximating function defined by composing more than one layer of simple functions. We study deep approximations of functions of one variable using layers consisting of low-degree polynomials or simple conformal…
Functional constraints and bi-functional constraints are an important constraint class in Constraint Programming (CP) systems, in particular for Constraint Logic Programming (CLP) systems. CP systems with finite domain constraints usually…
The present article is devoted to functions from a certain subclass of non-differentiable functions. The arguments and values of considered functions represented by the s-adic representation or the nega-s-adic representation of real…
We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure…
Regular functions from infinite words to infinite words can be equivalently specified by MSO-transducers, streaming $\omega$-string transducers as well as deterministic two-way transducers with look-ahead. In their one-way restriction, the…
Let k be an algebraically closed field of characteristic zero. An element F from k(x_1,...,x_n) is called a closed rational function if the subfield k(F) is algebraically closed in the field k(x_1,...,x_n). We prove that a rational function…
Marginalization -- summing a function over all assignments to a subset of its inputs -- is a fundamental computational problem with applications from probabilistic inference to formal verification. Despite its computational hardness in…
It was proved few years ago that classes of Boolean functions definable by means of functional equations \cite{EFHH}, or equivalently, by means of relational constraints \cite{Pi2}, coincide with initial segments of the quasi-ordered set…
How important is the weight of a given column in determining the ranking of tuples in a table? To address such an explanation question about a ranking function, we investigate the computation of SHAP scores for column weights, adopting a…
This paper is concerned with the study of the fractional finite sums theory. We present the classes of functions for which it is possible to characterize the constant related to the derivative of fractional sums (denominated by essence of a…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
For a given graph whose edges are labeled with general real numbers, we consider the set of functions from the vertex set into the Euclidean plane such that the distance between the images of neighbouring vertices is equal to the…
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the second in a series of papers in…
We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…