Article
Predecessors and Gardens of Eden in sequential dynamical systems over directed graphs
Authors
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Abstract
In this work, we deal with the predecessors existence problems in sequential dynamical systems over directed graphs. The results given in this paper extend those existing for such systems over undirected graphs. In particular, we solve the problems on the existence, uniqueness and coexistence of predecessors of any given state vector, characterizing the Garden-of-Eden states at the same time. We are also able to provide a bound for the number of predecessors and Garden-of-Eden state vectors of any of these systems.
Keywords
Sequential dynamical systems, Boolean functions, Predecessors, Garden-of-Eden points, 90B10, 37E15, 94C10, 94C15, 05A15
Citation
Aledo, J. A., Diaz, L. G., Martinez, S., & Valverde, J. C. (2018). Predecessors and gardens of eden in sequential dynamical systems over directed graphs. Applied Mathematics and Nonlinear Sciences, 3(2), 593–602. https://doi.org/10.2478/AMNS.2018.2.00046
J. A. Aledo, L. G. Diaz, S. Martinez and J. C. Valverde, “Predecessors and gardens of eden in sequential dynamical systems over directed graphs,” Applied Mathematics and Nonlinear Sciences, vol. 3, no. 2, pp. 593–602, 2018, doi: 10.2478/AMNS.2018.2.00046.
Aledo JA, Diaz LG, Martinez S, Valverde JC. Predecessors and gardens of eden in sequential dynamical systems over directed graphs. Applied Mathematics and Nonlinear Sciences. 2018;3(2):593–602. doi:10.2478/AMNS.2018.2.00046.
Aledo, J. A., Diaz, L. G., Martinez, S. and Valverde, J. C. (2018), ‘Predecessors and gardens of eden in sequential dynamical systems over directed graphs’, Applied Mathematics and Nonlinear Sciences, 3(2), pp. 593–602. Available at: https://doi.org/10.2478/AMNS.2018.2.00046.
Aledo, Juan A., et al. “Predecessors and Gardens of Eden in Sequential Dynamical Systems Over Directed Graphs.” Applied Mathematics and Nonlinear Sciences, vol. 3, no. 2, 2018, pp. 593–602. https://doi.org/10.2478/AMNS.2018.2.00046.
Aledo, Juan A., Luis G. Diaz, Silvia Martinez, and Jose C. Valverde. “Predecessors and Gardens of Eden in Sequential Dynamical Systems Over Directed Graphs.” Applied Mathematics and Nonlinear Sciences 3, no. 2 (2018): 593–602. https://doi.org/10.2478/AMNS.2018.2.00046.
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Published by: Engineering Journals
