Algebraic Structure and Complexity of Bootstrap Percolation with External Inputs
Dynamical Systems
2020-05-21 v1 Group Theory
Adaptation and Self-Organizing Systems
Abstract
In this paper a modification of the standard Bootstrap Percolation model is introduced. In our modification a discrete time update rule is constructed that allows for non-monotonicity - unlike its classical counterpart. External inputs to drive the system into desirable states are also included in the model. The algebraic structure and complexity properties of the system are inferred by studying the system's holonomy decomposition. We introduce methods of inferring the pools of reversibility for the system. Dependence of system complexity on process parameters is presented and discussed.
Cite
@article{arxiv.2005.10078,
title = {Algebraic Structure and Complexity of Bootstrap Percolation with External Inputs},
author = {Saptarshi Pal and Chrystopher L. Nehaniv},
journal= {arXiv preprint arXiv:2005.10078},
year = {2020}
}
Comments
10 pages, 5 Figures, Accepted with Minor Changes at Recent Advances in Mathematical and Statistical Methods, Proceedings of AMMCS - 2019