Symmetry and Algorithmic Complexity of Polyominoes and Polyhedral Graphs

Hector Zenil; Narsis A. Kiani; Jesper Tegnér

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arXiv · 1803.02186

Symmetry and Algorithmic Complexity of Polyominoes and Polyhedral Graphs

Hector Zenil·Narsis A. Kiani·Jesper Tegnér

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Abstract

We introduce a definition of algorithmic symmetry able to capture essential aspects of geometric symmetry. 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 enumeration 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 properties of polyominoes, polytopes, regular and quasi-regular polyhedra as well as polyhedral networks, thereby demonstrating its profiling capabilities.

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BibTeX RIS

Hector Zenil, Narsis A. Kiani, Jesper Tegnér. 2018-02-24. Symmetry and Algorithmic Complexity of Polyominoes and Polyhedral Graphs. https://arxiv.org/abs/1803.02186

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