Abstract
In place of the traditional definition of a cellular automaton CA = (S, Q, N, f), a new definition (S, Q, f n , ν) is given by introducing an injection called the neighborhood function ν: {0, 1,...,n − 1}→S, which provides a connection between the variables of local function f n of arity n and neighbors of CA: image(ν) is a neighborhood of size n. The new definition allows new analysis of cellular automata. We first show that from a single local function countably many CA are induced by changing ν and then prove that equivalence problem of such CA is decidable. Then we observe what happens if we change the neighborhood. As a typical research topics, we show that reversibility of 2 states 3 neighbors CA is preserved from changing the neighborhood, but that of 3 states CA is not.
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© 2007 Springer-Verlag Berlin Heidelberg
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Nishio, H. (2007). Changing the Neighborhood of Cellular Automata. In: Durand-Lose, J., Margenstern, M. (eds) Machines, Computations, and Universality. MCU 2007. Lecture Notes in Computer Science, vol 4664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74593-8_22
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DOI: https://doi.org/10.1007/978-3-540-74593-8_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74592-1
Online ISBN: 978-3-540-74593-8
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