Reversible cellular automata in presence of noise rapidly forget everything
Distributed, Parallel, and Cluster Computing
2022-03-21 v1 Emerging Technologies
Information Theory
math.IT
Probability
Cellular Automata and Lattice Gases
Abstract
We consider reversible and surjective cellular automata perturbed with noise. We show that, in the presence of positive additive noise, the cellular automaton forgets all the information regarding its initial configuration exponentially fast. In particular, the state of a finite collection of cells with diameter n becomes indistinguishable from pure noise after O(log n) time steps. This highlights the seemingly unavoidable need for irreversibility in order to perform scalable reliable computation in the presence of noise.
Keywords
Cite
@article{arxiv.2105.00725,
title = {Reversible cellular automata in presence of noise rapidly forget everything},
author = {Siamak Taati},
journal= {arXiv preprint arXiv:2105.00725},
year = {2022}
}
Comments
To appear in the Proceedings of AUTOMATA 2021, published in the OASIcs series