Bounds on Non-surjective Cellular Automata
نویسندگان
چکیده
Cellular automata (CA) are discrete, homogeneous dynamical systems. Non-surjective one-dimensional CA have nite words with no preimage (called orphans), pairs of di erent words starting and ending identically and having the same image (diamonds) and words with more/fewer preimages than the average number (unbalanced words). Using a linear algebra approach, we obtain new upper bounds on the lengths of the shortest such objects. In the case of an n-state, non-surjective CA with neighborhood range 2 our bounds are of the orders O(n), O(n) and O(n) for the shortest orphan, diamond and unbalanced word, respectively.
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