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The notion of Kolmogorov complexity (=the minimal length of a program that generates some object) is often useful as a kind of language that allows us to reformulate some notions and therefore provide new intuition. In this survey we…
Research into active networking has provided the incentive to re-visit what has traditionally been classified as distinct properties and characteristics of information transfer such as protocol versus service; at a more fundamental level…
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…
By Kolmogorov Complexity,two number-theoretic problems are solved in different way than before,one problem is Maxim Kontsevich and Don Bernard Zagier's Problem 3 \emph{Exhibit at least one number which does not belong to} $ \mathcal{P}$…
We study operator complexity on various time scales with emphasis on those much larger than the scrambling period. We use, for systems with a large but finite number of degrees of freedom, the notion of K-complexity employed in…
Although procedural generation is popular among game developers, academic research on the topic has primarily focused on new applications, with some research into empirical analysis. In this paper we relate theoretical work in information…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
In analogy of classical Kolmogorov complexity we develop a theory of the algorithmic information in bits contained in any one of continuously many pure quantum states: quantum Kolmogorov complexity. Classical Kolmogorov complexity coincides…
Kolmogorov Complexity constitutes an integral part of computability theory, information theory, and computational complexity theory -- in the discrete setting of bits and Turing machines. Over real numbers, on the other hand, the…
The ability to precisely quantify similarity between various entities has been a fundamental complication in various problem spaces specifically in the classification of cellular images. Contemporary similarity measures applied in the…
The paper studies randomness extraction from sources with bounded independence and the issue of independence amplification of sources, using the framework of Kolmogorov complexity. The dependency of strings $x$ and $y$ is ${\rm dep}(x,y) =…
The main goal of this paper is to put some known results in a common perspective and to simplify their proofs. We start with a simple proof of a result from (Vereshchagin, 2002) saying that $\limsup_n\KS(x|n)$ (here $\KS(x|n)$ is…
We review and investigate some new problems and results in the field of dynamical systems generated by iteration of maps, {\beta}-transformations, partitions, group actions, bundle dynamical systems, Hasse-Kloosterman maps, and some aspects…
An infinite binary sequence is Bennett deep if, for any computable time bound, the difference between the time-bounded prefix-free Kolmogorov complexity and the prefix-free Kolmogorov complexity of its initial segments is eventually…
We comment on a recent paper by D'Abramo [Chaos, Solitons & Fractals, 25 (2005) 29], focusing on the author's statement that an algorithm can produce a list of strings containing at least one string whose algorithmic complexity is greater…
In the first part of this paper, we present a unified framework for analyzing the algorithmic complexity of any optimization problem, whether it be continuous or discrete in nature. This helps to formalize notions like "input", "size" and…
The incompressibility method is a counting argument in the framework of algorithmic complexity that permits discovering properties that are satisfied by most objects of a class. This paper gives a preliminary insight into Kolmogorov's…
Kolmogorov complexity theory is used to tell what the algorithmic informational content of a string is. It is defined as the length of the shortest program that describes the string. We present a programming language that can be used to…
The state complexity of basic operations on finite languages (considering complete DFAs) has been in studied the literature. In this paper we study the incomplete (deterministic) state and transition complexity on finite languages of…
Reasoning with defeasible and conflicting knowledge in an argumentative form is a key research field in computational argumentation. Reasoning under various forms of uncertainty is both a key feature and a challenging barrier for automated…