A4 Refereed article in a conference publication
Commutators of Bipermutive and Affine Cellular Automata
Authors: Ville Salo, Ilkka Törmä
Editors: Jarkko Kari, Martin Kutrib, Andreas Malcher
Publishing place: Berlin
Publication year: 2013
Journal: Lecture Notes in Computer Science
Book title : Cellular Automata and Discrete Complex Systems: 19th International Workshop, AUTOMATA 2013, Gießen, Germany, September 14-19, 2013, Proceedings
Series title: Lecture Notes in Computer Science
Volume: 8155
First page : 155
Last page: 170
ISBN: 978-3-642-40866-3
eISBN: 978-3-642-40867-0
ISSN: 0302-9743
DOI: https://doi.org/10.1007/978-3-642-40867-0_11
Web address : http://dx.doi.org/10.1007/978-3-642-40867-0_11
Abstract
We discuss bipermutive cellular automata from a combinatorial and topological perspective. We prove a type of topological randomizing property for bipermutive CA, show that the commutator of a bipermutive CA is always small and that bipermutive affine CA have only ane CA in their commutator. We show the last result also in the multidimensional case, proving a conjecture of [Moore-Boykett, 97].
We discuss bipermutive cellular automata from a combinatorial and topological perspective. We prove a type of topological randomizing property for bipermutive CA, show that the commutator of a bipermutive CA is always small and that bipermutive affine CA have only ane CA in their commutator. We show the last result also in the multidimensional case, proving a conjecture of [Moore-Boykett, 97].
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