Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations

Hector Zenil, Narsis Kiani, Jesper Tegner

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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.
Original languageEnglish (US)
Pages (from-to)534
JournalEntropy
Volume20
Issue number7
DOIs
StatePublished - Jul 18 2018

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