Related papers: Functional Clones and Expressibility of Partition …
Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained…
Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…
We study the Potts model (defined geometrically in the cluster picture) on finite two-dimensional lattices of size L x N, with boundary conditions that are free in the L-direction and periodic in the N-direction. The decomposition of the…
Code clones are similar code fragments that often arise from copy-and-paste programming. Neural networks can classify pairs of code fragments as clone/not-clone with high accuracy. However, finding clones in industrial-scale code needs a…
Unlike polynomials, rational functions can represent functions having poles or branch cuts with root-exponential convergence and no Runge phenomenon. Recent developments of the AAA and greedy Thiele algorithms have sparked renewed interest…
We investigate the complexity of the Boolean clone membership problem (CMP): given a set of Boolean functions $F$ and a Boolean function $f$, determine if $f$ is in the clone generated by $F$, i.e., if it can be expressed by a circuit with…
The goal of the paper is to relate complexity measures associated with the evaluation of Boolean functions (certificate complexity, decision tree complexity) and learning dimensions used to characterize exact learning (teaching dimension,…
We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summands are defined with respect to different partial orders. We…
We consider holomorphic functions on the unit disc whose images are contained in a strip of the complex plane. Under an additional condition, such functions are constants. We also consider appropriate operator valued versions. Applications…
To convert a fractional solution to an instance of a constraint satisfaction problem into a solution, a rounding scheme is needed, which can be described by a collection of symmetric operations with one of each arity. An intriguing…
We study the complexity classes P and NP through a semigroup fP ("polynomial-time functions"), consisting of all polynomially balanced polynomial-time computable partial functions. Then P is not equal to NP iff fP is a non-regular…
This paper compares different representations (in the sense of computable analysis) of a number of function spaces that are of interest in analysis. In particular subspace representations inherited from a larger function space are compared…
Programmers often reuse code from source code repositories to reduce the development effort. Code clones are candidates for reuse in exploratory or rapid development, as they represent often repeated functionality in software systems. To…
A class is studied of complex valued functions defined on the unit disk (with a possible exception of a discrete set) with the property that all their Pick matrices have not more than a prescribed number of negative eigenvalues. Functions…
This paper outlines connections between Monotone Boolean Functions, LP-Type problems and the Maximum Consensus Problem. The latter refers to a particular type of robust fitting characterisation, popular in Computer Vision (MaxCon). Indeed,…
Many underlying structural and functional factors that determine the fault behavior of a combinational network, are not yet fully understood. In this paper, we show that there exists a large class of Boolean functions, called root…
Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…
The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…
A clone of functions on a finite domain determines and is determined by its system of invariant relations (=predicates). When a clone is determined by a finite number of relations, we say that the clone is of finite degree. For each Minsky…
Holant problem is a general framework to study the computational complexity of counting problems. We prove a complexity dichotomy theorem for Holant problems over Boolean domain with non-negative weights. It is the first complete Holant…