Related papers: Kolmogorov Complexity in perspective. Part II: Cla…
There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…
This Thesis explores the notion of Krylov complexity as a probe of quantum chaos and as a candidate for holographic complexity. The first Part is devoted to presenting the fundamental notions required to conduct research in this area.…
We present several application of simple topological arguments in problems of Kolmogorov complexity. Basically we use the standard fact from topology that the disk is simply connected. It proves to be enough to construct strings with some…
In this paper, a representation of the information-disturbance theorem based on the quantum Kolmogorov complexity that was defined by P. Vitanyi has been examined. In the quantum information theory, the information-disturbance relationship,…
This work presents a study of Kolmogorov complexity for general quantum states from the perspective of deterministic-control quantum Turing Machines (dcq-TM). We extend the dcq-TM model to incorporate mixed state inputs and outputs, and…
Kolmogorov complexity is often used as a convenient language for counting and/or probabilistic existence proofs. However, there are some applications where Kolmogorov complexity is used in a more subtle way. We provide one (somehow)…
This article introduces the conjecture that "mathematics, logic and related disciplines may usefully be understood as information compression (IC) by 'multiple alignment', 'unification' and 'search' (ICMAUS)". As a preparation for the two…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
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}$…
Link prediction in graphs is an important task in the fields of network science and machine learning. We investigate a flexible means of regularization for link prediction based on an approximation of the Kolmogorov complexity of graphs…
Data representation techniques have made a substantial contribution to advancing data processing and machine learning (ML). Improving predictive power was the focus of previous representation techniques, which unfortunately perform rather…
Physics concepts have often been borrowed and independently developed by other fields of science. In this perspective a significant example is that of entropy in Information Theory. The aim of this paper is to provide a short and…
Given two events $A$ and $B$, Bayes' law is based on the argument that the probability of $A$ given $B$ is proportional to the probability of $B$ given $A$. When probabilities are interpreted in the Bayesian sense, Bayes' law constitutes a…
In this survey, we explore Andrei Nikolayevich Kolmogorov's seminal work in just one of his many facets: its influence Computer Science especially his viewpoint of what herein we call 'Algorithmic Theory of Informatics.' Can a computer file…
In contrast to entropy, which increases monotonically, the "complexity" or "interestingness" of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex…
The problem of defining and studying complexity of a time series has interested people for years. In the context of dynamical systems, Grassberger has suggested that a slow approach of the entropy to its extensive asymptotic limit is a sign…
One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of…
It is a challenge to manage complex systems efficiently without confronting NP-hard problems. To address the situation we suggest to use self-organization processes of prime integer relations for information processing. Self-organization…
A number of generalizations of stochastic and information-theoretic randomness are known in the literature. However, they are not compatible with handling meaning in vague and dynamic contexts of rough reasoning (and therefore explainable…
This study proposes a low-complexity interpretable classification system. The proposed system contains three main modules including feature extraction, feature reduction, and classification. All of them are linear. Thanks to the linear…