Abstract
In this article, we discuss the family of cellular automata generated by so-called idempotent cellular automata (CA G such that G 2 = G) on the full shift. We prove a characterization of products of idempotent CA, and show examples of CA which are not easy to directly decompose into a product of idempotents, but which are trivially seen to satisfy the conditions of the characterization. Our proof uses ideas similar to those used in the well-known Embedding Theorem and Lower Entropy Factor Theorem in symbolic dynamics. We also consider some natural decidability questions for the class of products of idempotent CA.
Research supported by the Academy of Finland Grant 131558
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Salo, V. (2012). A Characterization of Cellular Automata Generated by Idempotents on the Full Shift. In: Hirsch, E.A., Karhumäki, J., Lepistö, A., Prilutskii, M. (eds) Computer Science – Theory and Applications. CSR 2012. Lecture Notes in Computer Science, vol 7353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30642-6_27
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DOI: https://doi.org/10.1007/978-3-642-30642-6_27
Publisher Name: Springer, Berlin, Heidelberg
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