Abstract
We study the sequential iteration of an automata class defined by local rules evolving only to local extreme values. Under the symmetry assumption of the cellular space we determine a Lyapunov operator driving the automaton dynamics. This operator allows us to characterize the steady state as a set of fixed points and to give bounds for the transient phase.
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References
W. Goddard and D.J. Kleitman, Convergence of a Transformation on a Weighted Graph.
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H.P. Kramer and J.B. Bruckner, Iterations of a Nonlinear Transformation for Enhancement of Digital Images, Pattern Recognition 7 (1975), 53–58.
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© 1993 Springer Science+Business Media Dordrecht
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Goles, E., Hernández, G. (1993). Sequential Iteration For Extremal Automata. In: Tirapegui, E., Zeller, W. (eds) Instabilities and Nonequilibrium Structures IV. Mathematics and Its Applications, vol 267. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1906-1_14
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DOI: https://doi.org/10.1007/978-94-011-1906-1_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4842-2
Online ISBN: 978-94-011-1906-1
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