How common can be universality for cellular automata?

Authors:
Guillaume Theyssier
Affiliations:
LIP (UMR CNRS, ENS Lyon, INRIA, Univ. Claude Bernard Lyon 1), École Normale Supérieure de Lyon, LYON, France
Venue:
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Year:
2005

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Abstract

We address the problem of the density of intrinsically universal cellular automata among cellular automata or a subclass of cellular automata. We show that captive cellular automata are almost all intrinsically universal. We show however that intrinsic universality is undecidable for captive cellular automata. Finally, we show that almost all cellular automata have no non-trivial sub-automaton.