JP Journal of Algebra, Number Theory and Applications
Volume 45, Issue 2, Pages 187 - 203
(February 2020) http://dx.doi.org/10.17654/NT045020187 |
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INJECTIVITY OF CELLULAR AUTOMATA (II)
Hiroyuki Ishibashi
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Abstract: This is a sequel of Ishibashi [2]. Let be a cellular automaton. We write for the set of configurations in and for the set of configurations of finite type in C. Further, let be the global map of and the restriction of F on
Then, in Ishibashi [2], we have shown that the noninjectivity of is equivalent to either the existence of a pair of mutually erasable configurations or the existence of a pair of nondistinguished configurations
In the present paper, we shall show that the above fact for is not true for F. To show it, we will construct a special cellular automaton Our main effort will be towards this construction.
As a result, we give a generalization of the theorem in Ishibashi [2]. |
Keywords and phrases: cellular automaton, tessellation space, global map of configurations, mutually erasable, Garden of Eden.
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