Symmetry and algorithmic complexity of polyominoes and polyhedral graphs

作     者：Zenil, Hector Kiani, Narsis A. Tegnér, Jesper 

作者机构：Algorithmic Dynamics Lab Centre for Molecular Medicine Karolinska Institute Stockholm Sweden Unit of Computational Medicine Department of Medicine Karolinska Institute Stockholm Sweden Science for Life Laboratory SciLifeLab Stockholm Sweden Algorithmic Nature Group LABORES for the Natural and Digital Sciences Paris France  Saudi Arabia 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2018年

核心收录：

主　　题：Topology 

摘      要：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 enumerate all properties of computable (causal) nature beyond statistical regularities. We explore the connections of al- gorithmic complexity|both theoretical and numerical| with geometric properties mainly symmetry and topology from an (algorithmic) information- theoretic perspective. We show that approximations to algorithmic com- plexity 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. Copyright © 2018, The Authors. All rights reserved.