Abstract
Cellular automata (CA) are discrete, homogeneous dynamical systems. Non-surjective one-dimensional CA have finite words with no preimage (called orphans), pairs of different 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 2), O(n 3/2) and O(n) for the shortest orphan, diamond and unbalanced word, respectively.
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Kari, J., Vanier, P., Zeume, T. (2009). Bounds on Non-surjective Cellular Automata. In: Královič, R., Niwiński, D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03816-7_38
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DOI: https://doi.org/10.1007/978-3-642-03816-7_38
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