Freezing sandpiles and Boolean threshold networks: equivalence and complexity

TL;DR

This paper explores the computational complexity of predicting sandpile dynamics by examining a freezing variant, revealing connections with Boolean threshold networks and highlighting key factors influencing complexity.

Contribution

It establishes a link between sandpile prediction problems and Boolean threshold networks, and identifies critical elements affecting dynamical complexity.

Findings

Connections between sandpile prediction and Boolean threshold networks

Role of cells with two grains in complexity

Progress on the open NC vs P-hard classification

Abstract

The NC versus P-hard classification of the prediction problem for sandpiles on the two dimensional grid with von Neumann neighborhood is a famous open problem. In this paper we make two kinds of progresses, by studying its freezing variant. First, it enables to establish strong connections with other well known prediction problems on networks of threshold Boolean functions such as majority. Second, we can highlight some necessary and sufficient elements to the dynamical complexity of sandpiles, with a surprisingly crucial role of cells with two grains.