The Mirage of Universality in Cellular Automata

12/02/2021
by   Guillaume Theyssier, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/15/2022

Cold Dynamics in Cellular Automata: a Tutorial

This tutorial is about cellular automata that exhibit 'cold dynamics'. B...
research
01/15/1998

On the classifiability of cellular automata

Based on computer simulations Wolfram presented in several papers conjec...
research
02/15/2019

Descriptive complexity for minimal time of cellular automata

Descriptive complexity may be useful to design programs in a natural dec...
research
04/20/2018

Universality in Freezing Cellular Automata

Cellular Automata have been used since their introduction as a discrete ...
research
08/18/2022

Embedding arbitrary Boolean circuits into fungal automata

Fungal automata are a variation of the two-dimensional sandpile automato...
research
10/23/2017

Conjugacy of one-dimensional one-sided cellular automata is undecidable

Two cellular automata are strongly conjugate if there exists a shift-com...
research
05/02/2021

Fixed Point Constructions in Tilings and Cellular Automata

The fixed point construction is a method for designing tile sets and cel...

Please sign up or login with your details

Forgot password? Click here to reset