<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

Predecessors and Gardens of Eden in sequential dynamical systems over directed graphs

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In this work, we deal with the predecessors existence problems in sequential dynamical systems over directed graphs. The results given in this paper extend...

Predecessors and Gardens of Eden in sequential dynamical systems over directed graphs

Published Online: Dec 31, 2018

Page range: 593 - 602

Received: Oct 12, 2018

Accepted: Dec 31, 2018

DOI: https://doi.org/10.2478/AMNS.2018.2.00046

Keywords
Sequential dynamical systems, Boolean functions, Predecessors, Garden-of-Eden points

© 2018 J.A. Aledo et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Predecessors and Gardens of Eden in sequential dynamical systems over directed graphs

Published Online: Dec 31, 2018

Page range: 593 - 602

Received: Oct 12, 2018

Accepted: Dec 31, 2018

DOI: https://doi.org/10.2478/AMNS.2018.2.00046

KeywordsSequential dynamical systems, Boolean functions, Predecessors, Garden-of-Eden points

© 2018 J.A. Aledo et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Sequential dynamical systems, Boolean functions, Predecessors, Garden-of-Eden points