Overview
- Provides recent research on evaluating the Kolmogorov complexity of short strings
- Presents an alternative to compression algorithms
- Written by leading experts in the field
Part of the book series: Emergence, Complexity and Computation (ECC, volume 44)
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Table of contents (9 chapters)
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Front Matter
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Applications
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Front Matter
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Back Matter
Keywords
About this book
This book explores a different pragmatic approach to algorithmic complexity rooted or motivated by the theoretical foundations of algorithmic probability and explores the relaxation of necessary and sufficient conditions in the pursuit of numerical applicability, with some of these approaches entailing greater risks than others in exchange for greater relevance and applicability.
Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently coexist for the first time, ranging from the dominant ones based upon popular statistical lossless compression algorithms (such as LZW) to newer approaches that advance, complement, and also pose their own limitations. Evidence suggesting that these different methods complement each other for different regimes is presented, and despite their many challenges, some of these methods are better grounded in or motivated by the principles of algorithmic information.
The authors propose that the field can make greater contributions to science, causation, scientific discovery, networks, and cognition, to mention a few among many fields, instead of remaining either as a technical curiosity of mathematical interest only or as a statistical tool when collapsed into an application of popular lossless compression algorithms. This book goes, thus, beyond popular statistical lossless compression and introduces a different methodological approach to dealing with algorithmic complexity.
For example, graph theory and network science are classic subjects in mathematics widely investigated in the twentieth century, transforming research in many fields of science from economy to medicine. However, it has become increasingly clear that the challenge of analyzing these networks cannot be addressed by tools relying solely on statistical methods. Therefore, model-driven approaches are needed. Recent advances in network science suggest that algorithmic informationtheory could play an increasingly important role in breaking those limits imposed by traditional statistical analysis (entropy or statistical compression) in modeling evolving complex networks or interacting networks. Further progress on this front calls for new techniques for an improved mechanistic understanding of complex systems, thereby calling out for increased interaction between systems science, network theory, and algorithmic information theory, to which this book contributes.
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Authors and Affiliations
Bibliographic Information
Book Title: Methods and Applications of Algorithmic Complexity
Book Subtitle: Beyond Statistical Lossless Compression
Authors: Hector Zenil, Fernando Soler Toscano, Nicolas Gauvrit
Series Title: Emergence, Complexity and Computation
DOI: https://doi.org/10.1007/978-3-662-64985-5
Publisher: Springer Berlin, Heidelberg
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag GmbH Germany, part of Springer Nature 2022
Hardcover ISBN: 978-3-662-64983-1Published: 17 May 2022
eBook ISBN: 978-3-662-64985-5Published: 16 May 2022
Series ISSN: 2194-7287
Series E-ISSN: 2194-7295
Edition Number: 1
Number of Pages: IX, 267
Number of Illustrations: 53 b/w illustrations, 55 illustrations in colour
Topics: Complexity, Computational Intelligence, Artificial Intelligence