Computational Complexity of the Avalanche Problem on One Dimensional Kadanoff Sandpiles

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

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-compl...

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

In this paper we prove that the avalanche problem for the 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-c...

Two Notes on the Computational Complexity of One-Dimensional Sandpiles

We prove that the one-dimensional sandpile prediction problem is in AC. The previously best known upper bound on the AC-scale was AC. We also prove that it is not in AC1− for any constant

Two Notes on the Computational Complexity of One-Dimensional Sandpiles

Relaxation oscillations in model sandpiles

We introduce a simple one-dimensional sandpile model that undergoes relaxation oscillations. A single model can account for self-organized critical behavior and relaxation oscillations, depending on the manner in which it is driven, mirroring the experimental situation for real sandpiles. The relaxation oscillations are robust with respect to minor modifications of the avalanche rules, includin...