Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations
KAUST DepartmentBiological and Environmental Sciences and Engineering (BESE) Division
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Permanent link to this recordhttp://hdl.handle.net/10754/631529
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AbstractWe 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.
CitationZenil 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.
SponsorsThis research was funded by Swedish Research Council (Vetenskapsrådet) grant number [2015-05299].
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