The Convergence of Symmetric Threshold Automata
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We study the length of the transient in a threshold automata with values on the set {0, 1~. The original conjecture was that in the symmetric case, this length was a linear function of the number of cells in the automata (Goles, E. (1981), “Comportement oscillatoire d'une famille d'automates cellulaires non uniformes,” These, IMAG, Grenoble, France; and Olivos, J. (1979), “Contribution a l'algorithmique,” These, Orsay, France). We shall show that this length can be exponential.
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