Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations
Type
ArticleKAUST Department
Biological and Environmental Sciences and Engineering (BESE) DivisionBioscience Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2018-07-18Permanent link to this record
http://hdl.handle.net/10754/631529
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We introduce a definition of algorithmic symmetry in the context of geometric and spatial complexity able to capture mathematical aspects of different objects using as a case study polyominoes and polyhedral graphs. We review, study and apply a method for approximating the algorithmic complexity (also known as Kolmogorov-Chaitin complexity) of graphs and networks based on the concept of Algorithmic Probability (AP). AP is a concept (and method) capable of recursively enumerate all properties of computable (causal) nature beyond statistical regularities. We explore the connections of algorithmic complexity-both theoretical and numerical-with geometric properties mainly symmetry and topology from an (algorithmic) information-theoretic perspective. We show that approximations to algorithmic complexity by lossless compression and an Algorithmic Probability-based method can characterize spatial, geometric, symmetric and topological properties of mathematical objects and graphs.Citation
Zenil H, Kiani N, Tegnér J (2018) Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations. Entropy 20: 534. Available: http://dx.doi.org/10.3390/e20070534.Sponsors
This research was funded by Swedish Research Council (Vetenskapsrådet) grant number [2015-05299].Publisher
MDPI AGJournal
EntropyAdditional Links
https://www.mdpi.com/1099-4300/20/7/534ae974a485f413a2113503eed53cd6c53
10.3390/e20070534
Scopus Count
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