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On the algorithmic complexity of crystals

Published online by Cambridge University Press:  05 July 2018

S. V. Krivovichev
S. V. Krivovichev*
Affiliation:
Department of Crystallography, Faculty of Geology, St. Petersburg State University, University Emb. 7/9, 199034 St. Petersburg, Russia Nanomaterials Research Centre, Kola Science Centre, Russian Academy of Sciences, Apatity, Russia
*
E-mail: [email protected]
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Abstract

The concept of the algorithmic complexity of crystals is developed for a particular class of minerals and inorganic materials based on orthogonal networks, which are defined as networks derived from the primitive cubic net (pcu) by the removal of some vertices and/or edges. Orthogonal networks are an important class of networks that dominate topologies of inorganic oxysalts, framework silicates and aluminosilicate minerals, zeolites and coordination polymers. The growth of periodic orthogonal networks may be modelled using structural automata, which are finite automata with states corresponding to vertex configurations and transition symbols corresponding to the edges linking the respective vertices. The model proposed describes possible relations between theoretical crystallography and theoretical computer science through the theory of networks and the theory of deterministic finite automata.

Keywords

crystal structuretopologyalgorithmic complexityorthogonal networksfinite state automatazeolitesinorganic oxysaltsformal languages
Type
Research Article
Information
Mineralogical Magazine , Volume 78 , Issue 2 , April 2014 , pp. 415 - 435
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 2014

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