Abstract
This paper analyzes the possible limit set structures for the standard threshold block-sequential finite dynamical systems. As a special case of their work on Neural Networks (generalized threshold functions), Goles and Olivos (1981 [2]) showed that for the single block case (parallel update) one may only have fixed points and 2-cycles as ω-limit sets. Barrett et al (2006 [1]), but also Goles et al (1990 [3]) as a special case, proved that for the case with n blocks (sequential update) the only ω-limit sets are fixed points. This paper generalizes and unifies these results to standard threshold systems with block-sequential update schemes.
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Mortveit, H.S. (2012). Limit Cycle Structure for Block-Sequential Threshold Systems. In: Sirakoulis, G.C., Bandini, S. (eds) Cellular Automata. ACRI 2012. Lecture Notes in Computer Science, vol 7495. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33350-7_69
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DOI: https://doi.org/10.1007/978-3-642-33350-7_69
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33349-1
Online ISBN: 978-3-642-33350-7
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