Kolmogorov's legacy: Algorithmic Theory of Informatics and Kolmogorov Programmable Technology
Sergei Levashkin (Artificial Intelligence Lab, Moscow. Russia), Victor, Alexandrov (Russian Academy of Sciences, Saint Petersburg, Russia), Adolfo, Guzm\'an-Arenas (Instituto Polit\'ecnico Nacional, Mexico City, Mexico)

TL;DR
This survey examines Kolmogorov's influence on computer science, emphasizing his ideas on algorithmic information theory, and proposes a new framework called Kolmogorov Programmable Technology that redefines mathematical approaches in computing.
Contribution
It introduces the concept of Kolmogorov Programmable Technology, integrating Kolmogorov's ideas into modern information technology and computer mathematics.
Findings
Kolmogorov's concepts underpin a new approach to computer science.
The paper formalizes Kolmogorov's ideas within modern computational frameworks.
It proposes a novel mathematical foundation called Komputer Mathematics.
Abstract
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 'reduce' its 'size' if we add to it new symbols? Do equations of state like second Newton law in Physics exist in Computer Science? Can Leibniz' principle of identification by indistinguishability be formalized? In the computer, there are no coordinates, no distances, and no dimensions; most of traditional mathematical approaches do not work. The computer processes finite binary sequences i.e. the sequences of 0 and 1. A natural question arises: Should we continue today, as we have done for many years, to approach Computer Science problems by using classical mathematical apparatus such as 'mathematical modeling'? The first who drew attention to…
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Cellular Automata and Applications · Logic, programming, and type systems
