Abstract
This paper consists of two parts. In the first we pick up again the question under which circumstances different pairs of a local function and a neighborhood give rise to the same global behavior of CA and disprove a conjecture made in an earlier paper. In the second part we reconsider a construction showing that one can achieve universality by only changing the (positions in the) neighborhood of a CA, while not providing any information about the CA to be simulated in the initial configuration. The construction uses an embedding which in some sense is “non-local”. We show that under mild conditions this is necessary.
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Worsch, T., Nishio, H. (2008). Changing Neighborhoods of CA: Reduced Local Structures and Embeddings for Universality. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds) Cellular Automata. ACRI 2008. Lecture Notes in Computer Science, vol 5191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79992-4_32
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DOI: https://doi.org/10.1007/978-3-540-79992-4_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79991-7
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