Related papers: On Nelson Goodman's final formulae for Primary Com…
The concept of effective complexity of an object as the minimal description length of its regularities has been initiated by Gell-Mann and Lloyd. The regularities are modeled by means of ensembles, that is probability distributions on…
This paper studies the complexity of determining whether a formula in the modal logics characterizing the nested-simulation semantics is characteristic for some process, which is equivalent to determining whether the formula is satisfiable…
How to measure the complexity of a finite set of vectors embedded in a multidimensional space? This is a non-trivial question which can be approached in many different ways. Here we suggest a set of data complexity measures using universal…
We estimate the Boolean complexity of multiplication of structured matrices by a vector and the solution of nonsingular linear systems of equations with these matrices. We study four basic most popular classes, that is, Toeplitz, Hankel,…
We investigate the end extendibility of models of arithmetic with restricted elementarity. By utilizing the restricted ultrapower construction in the second-order context, for each $n\in\mathbb{N}$ and any countable model of…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…
We consider the robustness of computational hardness of problems whose input is obtained by applying independent random deletions to worst-case instances. For some classical $NP$-hard problems on graphs, such as Coloring, Vertex-Cover, and…
Many systems of interest in cryptography consist of equations of the same degree. Under the assumption that the degree of regularity is finite, we prove upper bounds on the degree of regularity of a system of equations of the same degree,…
The minimization problem for propositional formulas is an important optimization problem in the second level of the polynomial hierarchy. In general, the problem is Sigma-2-complete under Turing reductions, but restricted versions are…
Since the introduction of strong anticipation by D.~Dubois the numerous investigations of concrete systems have been proposed. In proposed paper the new examples of discrete dynamical systems with anticipation are considered. The…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
We show that most arithmetic circuit lower bounds and relations between lower bounds naturally fit into the representation-theoretic framework suggested by geometric complexity theory (GCT), including: the partial derivatives technique…
Regression methods are fundamental for scientific and technological applications. However, fitted models can be highly unreliable outside of their training domain, and hence the quantification of their uncertainty is crucial in many of…
Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the…
Fully automatic worst-case complexity analysis has a number of applications in computer-assisted program manipulation. A classical and powerful approach to complexity analysis consists in formally deriving, from the program syntax, a set of…
We present in this paper a general algorithm for solving first-order formulas in particular theories called "decomposable theories". First of all, using special quantifiers, we give a formal characterization of decomposable theories and…
Using a regularization by putting the system in finite volume, we develop a novel approach to form factor perturbation theory for nonintegrable models described as perturbations of integrable ones. This permits to go beyond first order in…
We consider a problem first proposed by Mahler and Popken in 1953 and later developed by Coppersmith, Erd\H{o}s, Guy, Isbell, Selfridge, and others. Let $f(n)$ be the complexity of $n \in \mathbb{Z^{+}}$, where $f(n)$ is defined as the…
This article considers the problem of solving a system of $n$ real polynomial equations in $n+1$ variables. We propose an algorithm based on Newton's method and subdivision for this problem. Our algorithm is intended only for nondegenerate…