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Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically) universal CA, that is CA able to fully simulate any other CA. In this paper, we show that the asymptotic density of… (More)

We study the notion of limit sets of cellular automata associated with probability measures (µ-limit sets). This notion was introduced by P. Kůrka and A. Maass in [1]. It is a refinement of the classical notion of ω-limit sets dealing with the typical long term behavior of cellular au-tomata. It focuses on the words whose probability of appearance does not… (More)

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… (More)

This paper is about µ-limit sets of cellular automata, i.e. sets of congurations made of words which have a positive probability to appear arbitrarily late in the evolution, starting from an initial µ-random conguration. More precisely, we investigate the computational complexity of these sets and of decision problems concerning them. Our main results are:… (More)

- Laurent Boyer
- 2010

The µ-limit set of a cellular automaton is a subshift whose forbidden patterns are exactly those, whose probabilities tend to zero as time tends to infinity. In this article, for a given subshift in a large class of subshifts, we propose the construction of a cellular automaton which realizes this subshift as µ-limit set where µ is the uniform Bernoulli… (More)

Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically) universal CA, that is CA able to fully simulate any other CA. In this paper, we show that the asymptotic density of… (More)

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