The nilpotency problem of one-dimensional cellular automata
SIAM Journal on Computing
The Quest for Small Universal Cellular Automata
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
The Intrinsic Universality Problem of One-Dimensional Cellular Automata
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Intrinsic Universality of a 1-Dimensional Reversible Cellular Automaton
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Universality and decidability of number-conserving cellular automata
Theoretical Computer Science - Algorithms,automata, complexity and games
Theory of Self-Reproducing Automata
Theory of Self-Reproducing Automata
Theoretical Computer Science
An Almost Totally Universal Tile Set
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Subshifts as models for MSO logic
Information and Computation
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The study of factoring relations between subshifts or cellular automata is central in symbolic dynamics. Besides, a notion of intrinsic universality for cellular automata based on an operation of rescaling is receiving more and more attention in the literature. In this paper, we propose to study the factoring relation up to rescalings, and ask for the existence of universal objects for that simulation relation. In classical simulations of a system S by a system T, the simulation takes place on a specific subset of configurations of T depending on S (this is the case for intrinsic universality). Our setting, however, asks for every configurations of T to have a meaningful interpretation in S. Despite this strong requirement, we show that there exists a cellular automaton able to simulate any other in a large class containing arbitrarily complex ones. We also consider the case of subshifts and, using arguments from recursion theory, we give negative results about the existence of universal objects in some classes.