Index permutations and classes of additive cellular automata rules with isomorphic STD

Bulitko, V., Voorhees, B., Alonso-Sanz, R., Bull, L., Anghelescu, P., Ionita, S., Sofron, E., Clarridge, A., Salomaa, K. and Jin, W. (2010) Index permutations and classes of additive cellular automata rules with isomorphic STD. Journal of Cellular Automata, 5 (1-2). pp. 1-28. ISSN 1557-5969 Available from:

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First we consider the question of identifying linear transformations that transform any additive CA rule into an additive CA rule with an isomorphic STD. A general condition is derived. Following on this, we consider a subclass of such transformations (index permutations). This allows, on one hand, a complete description and on the other hand, generalization of the results for the class of linear rules. Then the case of binary valued 1-dimensional additive cellular automata (d = 1, p = 2) and classes of isomorphisms of STDs that contain only a single rule (singletons) are considered. It is shown how singletons can be used to extend known systems of isomorphic STD classes. Finally we study how the baker transformation provides information about singletons and, by using this, present an algorithm that generates all singletons for one-dimensional additive CA of odd sizes.

Item Type:Article
Uncontrolled Keywords:discrete baker transformation, mathematics, interdisciplinary applications, additive cellular automata, computer science, theory and methods, isomorphic classes, dynamics, state transition diagram
Faculty/Department:Faculty of Environment and Technology > Department of Computer Science and Creative Technologies
ID Code:20686
Deposited By: M. Clarke
Deposited On:24 Jul 2013 14:09
Last Modified:15 Nov 2016 22:20

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