Algebraic Structure and Complexity of Bootstrap Percolation with External Inputs

TL;DR

This paper introduces a modified bootstrap percolation model with non-monotonic updates and external inputs, analyzing its algebraic structure and complexity through holonomy decomposition and reversibility pools.

Contribution

It presents a novel non-monotonic bootstrap percolation model with external inputs and provides an algebraic analysis of its complexity and reversibility properties.

Findings

System complexity depends on process parameters

Holonomy decomposition reveals algebraic structure

Reversibility pools characterize system behavior

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.