Computational Complexity of Avalanches in the Kadanoff two-dimensional Sandpile Model

TL;DR

This paper proves that determining avalanches in the two-dimensional Kadanoff sandpile model is P-complete, indicating high computational complexity, by reducing from the monotone circuit value problem.

Contribution

It establishes the P-completeness of the avalanche problem for 2D Kadanoff sandpiles, advancing understanding of their computational complexity.

Findings

Avalanche problem for 2D Kadanoff sandpiles is P-complete.

Reduction from monotone circuit value problem demonstrates computational hardness.

Related to prediction problems in sandpile models across dimensions.

Abstract

In this paper we prove that the avalanche problem for Kadanoff sandpile model (KSPM) is P-complete for two-dimensions. Our proof is based on a reduction from the monotone circuit value problem by building logic gates and wires which work with configurations in KSPM. The proof is also related to the known prediction problem for sandpile which is in NC for one-dimensional sandpiles and is P-complete for dimension 3 or greater. The computational complexity of the prediction problem remains open for two-dimensional sandpiles.