In this work we introduce a wide generalization of dynamical systems over graphs, by considering that the states of the entities can take values in an arbitrary Boolean algebra with 2p elements, p ∈ N, p ≥ 1. Then the orbit structure of these more general parallel dynamical systems over undirected graphs where the evolution operator is an arbitrary maxterm or minterm is analyzed. Finally, we also study the cases of parallel dynamical systems whose evolution update is defined by means of independent local Boolean functions.
A. Aledo, Juan; Martinez, S.; and C. Valverde, Jose
"Graph Dynamical Systems with General Boolean States,"
Applied Mathematics & Information Sciences: Vol. 09:
4, Article 17.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss4/17