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Kolmogorov Complexity and Applications: Theoretical Achievements and Practical Tools

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: 30 January 2026 | Viewed by 1043

Special Issue Editor


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Guest Editor
1. Faculty of Agriculture, University of Novi Sad, 21000 Novi Sad, Serbia
2. Faculty of Sciences, Department of Physics, University of Novi Sad, 21000 Novi Sad, Serbia
Interests: complex systems; information theory; chaos theory; behavior of ultracold gases; UV radiation; modeling of environmental interfaces; climate modeling; environmental physics; psychophysics

Special Issue Information

Dear Colleagues,

In 1965, A.N. Kolmogorov introduced the Kolmogorov complexity concept in his foundational paper, "Three Approaches to the Definition of the Amount of Information", published in the Russian journal Problems of Information Transmission (Проблемы передачи информации, Т. 1, № 1. С. 3–11; later translated into several journals in English). This paper laid the groundwork for a formal understanding of algorithmic complexity and its implications in information theory. 

This only natural but uncomputable information measure is widely applied in intellectual activities of the human mind such as mathematics, the sciences, and art, touching the philosophical issues of its nature. Kolmogorov's complexity has more than a few applications across those activities. Here are some of the notable applications: Machine Learning and Data Analysis, Cryptography, Theoretical Computer Science, Information Theory, Quantum Computing, and practical tools based on the Kolmogorov complexity (Lempel-Ziv algorithm, Kolmogorov complexity spectrum, etc.). 

In this Special Issue, we are interested in original research discussing the theoretical aspects and practical tools with Kolmogorov complexity in the background focusing on (i) the understanding of complex systems and (ii) the analysis of the complexity of time series that come from measurements in sciences and art.

Prof. Dr. Dragutin T. Mihailović
Guest Editor

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Keywords

  • information theory
  • machine learning and data analysis
  • quantum computing
  • cryptography
  • Lempel–Ziv algorithm (engineering, geosciences, cardiology, neurology oncology, image analysis, language)
  • Kolmogorov complexity spectrum (astrophysics and cosmology, Bell's experiment, earth sciences, financial issues, psychophysics, and philosophical issues)

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Published Papers (2 papers)

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Research

16 pages, 4143 KB  
Article
Assessing the Role of Socio-Demographic Triggers on Kolmogorov-Based Complexity in Spoken English Varieties
by Katharina Ehret
Entropy 2025, 27(10), 1009; https://doi.org/10.3390/e27101009 - 26 Sep 2025
Viewed by 244
Abstract
This paper assesses the role of socio-demographic triggers on Kolmogorov-based complexity in spoken English varieties. It thus contributes to the ongoing debate on contact and complexity in the sociolinguistic typological research community. Currently, evidence on whether socio-demographic triggers influence the morphosyntactic complexity of [...] Read more.
This paper assesses the role of socio-demographic triggers on Kolmogorov-based complexity in spoken English varieties. It thus contributes to the ongoing debate on contact and complexity in the sociolinguistic typological research community. Currently, evidence on whether socio-demographic triggers influence the morphosyntactic complexity of languages is controversial and inconclusive. Particularly controversial is the influence of the proportion of non-native speakers and the number of native speakers, which are both common proxies for language contact. In order to illuminate the issue from an English-varieties perspective, I use regression analysis to test several socio-demographic triggers in a corpus database of spoken English varieties. Language complexity here is operationalised in terms of Kolmogorov-based morphological and syntactic complexity. The results only partially support the idea that socio-demographic triggers influence morphosyntactic complexity in English varieties, i.e., speaker-related triggers turn out to be negative but non-significant. Yet, net migration rate shows a positive significant effect on morphological complexity which needs to be seen in the global context of English as a commodity and unequal access to English. I thus argue that socioeconomic triggers are better predictors for complexity than demographic speaker numbers. In sum, the paper opens up new horizons for research on language complexity. Full article
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26 pages, 6893 KB  
Article
Exploring Overall and Component Complexities via Relative Complexity Change and Interacting Complexity Amplitudes in the Kolmogorov Plane: A Case Study of U.S. Rivers
by Dragutin T. Mihailović and Slavica Malinović-Milićević
Entropy 2025, 27(10), 1006; https://doi.org/10.3390/e27101006 - 26 Sep 2025
Viewed by 190
Abstract
One of the most challenging tasks in studying streamflow is quantifying how the complexities of environmental and dynamic parameters contribute to the overall system complexity. To address this, we employed Kolmogorov complexity (KC) metrics, specifically the Kolmogorov complexity spectrum (KC spectrum) and the [...] Read more.
One of the most challenging tasks in studying streamflow is quantifying how the complexities of environmental and dynamic parameters contribute to the overall system complexity. To address this, we employed Kolmogorov complexity (KC) metrics, specifically the Kolmogorov complexity spectrum (KC spectrum) and the Kolmogorov complexity plane (KC plane). These measures were applied to monthly streamflow time series averaged across 1879 gauge stations on U.S. rivers over the period 1950–2015. The variables analyzed included streamflow as a complex physical system, along with its key components: temperature, precipitation, and the Lyapunov exponent (LEX), which represents river dynamics. Using these metrics, we calculated normalized KC spectra for each position within the KC plane, visualizing interactive master amplitudes alongside individual amplitudes on overlapping two-dimensional planes. We further computed the relative change in complexities (RCC) of the normalized master and individual components within the KC plane, ranging from 0 to 1 in defined intervals. Based on these results, we analyzed and discussed the complexity patterns of U.S. rivers corresponding to each interval of normalized amplitudes. Full article
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