In this article, we discuss the family of cellular automata generated by so-called idempotent cellular automata (CA G such that G2 = 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.
Cellular Automaton Periodic Point Symbolic Dynamic Spreading State Decidability Question
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