Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations.
Entropy (Basel)
; 20(7)2018 Jul 18.
Article
en En
| MEDLINE
| ID: mdl-33265623
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.
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Colección:
01-internacional
Base de datos:
MEDLINE
Idioma:
En
Revista:
Entropy (Basel)
Año:
2018
Tipo del documento:
Article
País de afiliación:
Suecia