Kolmogorov Complexity and Applications: Theoretical Achievements and Practical Tools

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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