The Mirage of Universality in Cellular Automata
Computational Complexity
2021-12-03 v1 Discrete Mathematics
Dynamical Systems
Abstract
This note is a survey of examples and results about cellular automata with the purpose of recalling that there is no 'universal' way of being computationally universal. In particular, we show how some cellular automata can embed efficient but bounded computation, while others can embed unbounded computations but not efficiently. We also study two variants of Boolean circuit embedding, transient versus repeatable simulations, and underline their differences. Finally we show how strong forms of universality can be hidden inside some seemingly simple cellular automata according to some classical dynamical parameters.
Keywords
Cite
@article{arxiv.2112.01090,
title = {The Mirage of Universality in Cellular Automata},
author = {Guillaume Theyssier},
journal= {arXiv preprint arXiv:2112.01090},
year = {2021}
}