Related papers: Compression of enumerations and gain

Compression of integer sets and sequences has been extensively studied for settings where elements follow a uniform probability distribution. In addition, methods exist that exploit clustering of elements in order to achieve higher…

The ability to find short representations, i.e. to compress data, is crucial for many intelligent systems. We present a theory of incremental compression showing that arbitrary data strings, that can be described by a set of features, can…

We study connections between classical asymptotic density and c.e. sets. We prove that a c.e. Turing degree d is not low if and only if d contains a c.e. set A of density 1 which has no computable subsets of density 1, giving a natural…

The Kolmogorov complexity of x, denoted C(x), is the length of the shortest program that generates x. For such a simple definition, Kolmogorov complexity has a rich and deep theory, as well as applications to a wide variety of topics…

We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…

Ensemble models (bagging and gradient-boosting) of relational decision trees have proved to be one of the most effective learning methods in the area of probabilistic logic models (PLMs). While effective, they lose one of the most important…

Learning Spaces are certain set systems that are applied in the mathematical modeling of education. We propose a suitable compression (without loss of information) of such set systems to facilitate their logical and statistical analysis.…

We study the computably enumerable sets in terms of the: (a) Kolmogorov complexity of their initial segments; (b) Kolmogorov complexity of finite programs when they are used as oracles. We present an extended discussion of the existing…

We introduce the broad subclass of algebraic compressed sensing problems, where structured signals are modeled either explicitly or implicitly via polynomials. This includes, for instance, low-rank matrix and tensor recovery. We employ…

A real number is called left-computable if there exists a computable increasing sequence of rational numbers converging to it. In this article we investigate the Kolmogorov complexity and the binary expansions of a very specific subset of…

A relatively new topic in computability theory is the study of notions of computation that are robust against mistakes on some kind of small set. However, despite the recent popularity of this topic relatively foundational questions about…

Model compression is generally performed by using quantization, low-rank approximation or pruning, for which various algorithms have been researched in recent years. One fundamental question is: what types of compression work better for a…

The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…

The study of sums of finite sets of integers has mostly concentrated on sets with small sumsets (Freiman's theorem and related work) and on sets with large sumsets (Sidon sets and $B_h$-sets). This paper considers the sets ${\mathcal…

For which sets A does there exist a mapping, computed by a total or partial recursive function, such that the mapping, when its domain is restricted to A, is a 1-to-1, onto mapping to $\Sigma^*$? And for which sets A does there exist such a…

Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently co-exist for the first time and are here reviewed, ranging from dominant ones such as statistical lossless compression…

We address the problem of nonparametric estimation of characteristics for stationary and ergodic time series. We consider finite-alphabet time series and real-valued ones and the following four problems: i) estimation of the (limiting)…

Much work on argument systems has focussed on preferred extensions which define the maximal collectively defensible subsets. Identification and enumeration of these subsets is (under the usual assumptions) computationally demanding. We…

Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…

We establish diverse relationships between the algorithmic (Kolmogorov) complexity of the prefixes of any binary expansion and $\beta$-expansions. These relationships allow to develop intuitions on the complexity behavior of…