On Stable and Unstable Limit Sets of Finite Families of Cellular Automata

2012 ◽  
pp. 502-513
Author(s):  
Ville Salo ◽  
Ilkka Törmä
Keyword(s):  
Cellular Automata ◽  
Limit Sets

scholarly journals μ-Limit sets of cellular automata from a computational complexity perspective

2015 ◽  
Vol 81 (8) ◽  
pp. 1623-1647 ◽  
Author(s):  
L. Boyer ◽  
M. Delacourt ◽  
V. Poupet ◽  
M. Sablik ◽  
G. Theyssier
Keyword(s):  
Computational Complexity ◽  
Cellular Automata ◽  
Limit Sets

Limit Sets of Stable and Unstable Cellular Automata

2011 ◽  
Vol 110 (1-4) ◽  
pp. 45-57 ◽  
Author(s):  
Alexis Ballier ◽  
Pierre Guillon ◽  
Jarkko Kari
Keyword(s):  
Cellular Automata ◽  
Limit Sets

On the Limit Sets of Cellular Automata

1989 ◽  
Vol 18 (4) ◽  
pp. 831-842 ◽  
Author(s):  
Karel Culik II ◽  
Jan Pachl ◽  
Sheng Yu
Keyword(s):  
Cellular Automata ◽  
Limit Sets

scholarly journals Limit sets of stable cellular automata

2013 ◽  
Vol 35 (3) ◽  
pp. 673-690 ◽  
Author(s):  
ALEXIS BALLIER
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Point Of View ◽  
Limit Set ◽  
Limit Sets ◽  
Sofic Shift ◽  
Almost Everywhere ◽  
Sofic Shifts ◽  
Full Shift ◽  
Factor Map

AbstractWe study limit sets of stable cellular automata from a symbolic dynamics point of view, where they are a special case of sofic shifts admitting a steady epimorphism. We prove that there exists a right-closing almost-everywhere steady factor map from one irreducible sofic shift onto another one if and only if there exists such a map from the domain onto the minimal right-resolving cover of the image. We define right-continuing almost-everywhere steady maps, and prove that there exists such a steady map between two sofic shifts if and only if there exists a factor map from the domain onto the minimal right-resolving cover of the image. To translate this into terms of cellular automata, a sofic shift can be the limit set of a stable cellular automaton with a right-closing almost-everywhere dynamics onto its limit set if and only if it is the factor of a full shift and there exists a right-closing almost-everywhere factor map from the sofic shift onto its minimal right-resolving cover. A sofic shift can be the limit set of a stable cellular automaton reaching its limit set with a right-continuing almost-everywhere factor map if and only if it is the factor of a full shift and there exists a factor map from the sofic shift onto its minimal right-resolving cover. Finally, as a consequence of the previous results, we provide a characterization of the almost of finite type shifts (AFT) in terms of a property of steady maps that have them as range.

scholarly journals Rice's theorem for the limit sets of cellular automata

1994 ◽  
Vol 127 (2) ◽  
pp. 229-254 ◽  
Author(s):  
Jarkko Kari
Keyword(s):  
Cellular Automata ◽  
Limit Sets
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