Related papers: Functional Clones and Expressibility of Partition …
Let L be a bounded distributive lattice. We give several characterizations of those L^n --> L mappings that are polynomial functions, i.e., functions which can be obtained from projections and constant functions using binary joins and…
Coverage functions are an important subclass of submodular functions, finding applications in machine learning, game theory, social networks, and facility location. We study the complexity of partial function extension to coverage…
This paper is devoted to a study of mathematical structures arising from choice functions satisfying the path independence property (Plott functions). We broaden the notion of a choice function by allowing of empty choice. This enables us…
We introduce a general unifying framework for the investigation of pointlike sets. The pointlike functors are considered as distinguished elements of a certain lattice of subfunctors of the power semigroup functor; in particular, we exhibit…
The subject of this textbook is the analysis of Boolean functions. Roughly speaking, this refers to studying Boolean functions $f : \{0,1\}^n \to \{0,1\}$ via their Fourier expansion and other analytic means. Boolean functions are perhaps…
A unary constraint (on the Boolean domain) is a function from {0,1} to the set of real numbers. A free use of auxiliary unary constraints given besides input instances has proven to be useful in establishing a complete classification of the…
The input of most clustering algorithms is a symmetric matrix quantifying similarity within data pairs. Such a matrix is here turned into a quadratic set function measuring cluster score or similarity within data subsets larger than pairs.…
Overlap functions were introduced as class of bivariate aggregation functions on [0, 1] to be applied in image processing. This paper has as main objective to present appropriates definitions of overlap functions considering the scope of…
A key fact in the theory of Boolean functions $f : \{0,1\}^n \to \{0,1\}$ is that they often undergo sharp thresholds. For example: if the function $f : \{0,1\}^n \to \{0,1\}$ is monotone and symmetric under a transitive action with…
We investigate when the clone of congruence preserving functions is finitely generated. We obtain a full description for all finite $p$-groups, and for all finite algebras with Mal'cev term and simple congruence lattice. The…
We study the degrees of selector functions related to the degrees in which a rigid computable structure is relatively computably categorical. It is proved that for some structures such degrees can be represented as the unions of upper cones…
We investigate finitary functions from $\mathbb{Z}_{pq}$ to $\mathbb{Z}_{pq}$ for two distinct prime numbers $p$ and $q$. We show that the lattice of all clones on the set $\mathbb{Z}_{pq}$ which contain the addition of $\mathbb{Z}_{pq}$ is…
This paper reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by (a…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
We consider the problem of linearizing a pseudo-Boolean function $f : \{0,1\}^n \to \mathbb{R}$ by means of $k$ Boolean functions. Such a linearization yields an integer linear programming formulation with only $k$ auxiliary variables. This…
We analyse the complexity of approximate counting constraint satisfactions problems $\mathrm{\#CSP}(\mathcal{F})$, where $\mathcal{F}$ is a set of nonnegative rational-valued functions of Boolean variables. A complete classification is…
Code clone detection is involved with detecting duplicated fragments of code within a code base. Detecting these clones is useful for maintenance operations which require editing the clones. The tools developed are expected to be robust…
We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…
The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple…
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.