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Bulitko, V., Voorhees, B., AlonsoSanz, 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 (12). pp. 128. ISSN 15575969 Available from: http://eprints.uwe.ac.uk/20686 Full text not available from this repository Publisher's URL: http://www.oldcitypublishing.com/ Abstract/DescriptionFirst 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 1dimensional 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 onedimensional additive CA of odd sizes.
