The nilpotency problem of one-dimensional cellular automata
SIAM Journal on Computing
Rice's theorem for the limit sets of cellular automata
Theoretical Computer Science
An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
Theoretical Computer Science
Conservation of some dynamical properties for operations on cellular automata
Theoretical Computer Science
On the directional dynamics of additive cellular automata
Theoretical Computer Science
Some formal properties of asynchronous callular automata
ACRI'10 Proceedings of the 9th international conference on Cellular automata for research and industry
Non-uniform cellular automata: Classes, dynamics, and decidability
Information and Computation
On the Undecidability of Attractor Properties for Cellular Automata
Fundamenta Informaticae - From Physics to Computer Science: to Gianpiero Cattaneo for his 70th birthday
From One-dimensional to Two-dimensional Cellular Automata
Fundamenta Informaticae - From Physics to Computer Science: to Gianpiero Cattaneo for his 70th birthday
Surjective multidimensional cellular automata are non-wandering: A combinatorial proof
Information Processing Letters
Local rule distributions, language complexity and non-uniform cellular automata
Theoretical Computer Science
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Cellular Automata (CA) are discrete dynamical systems and an abstract model of parallel computation. The limit set of a cellular automaton is its maximal topological attractor. A well-known result, due to Kari, says that all nontrivial properties of limit sets are undecidable. In this paper we consider the properties of limit set dynamics, i.e. properties of the dynamics of CA restricted to their limit sets. There can be no equivalent of Kari's theorem for limit set dynamics. Anyway we show that there is a large class of undecidable properties of limit set dynamics, namely all properties of limit set dynamics which imply stability or the existence of a unique subshift attractor. As a consequence we have that it is undecidable whether the cellular automaton map restricted to the limit set is the identity map and whether it is closing, injective, expansive, positively expansive and transitive.