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On the Synchronisation Problem over Cellular Automata

Gaétan Richard 1
1 Equipe AMACC - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : Cellular automata are a discrete, synchronous, and uniform dynamical system that give rise to a wide range of dynamical behaviours. In this paper, we investigate whether this system can achieve synchronisation. We study the cases of classical bi-infinite configurations, periodic configurations, and periodic configurations of prime period. In the two former cases, we prove that only a "degenerated" form of synchronisation-there exists a fix-point-is possible. In the latter case, we give an explicit construction of a cellular automaton for which any periodic configuration of prime period eventually converges to cycle of two uniform configurations. Our construction is based upon sophisticated tools: aperiodic NW-deterministic tilings [7] and partitioned intervals [1].
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Gaétan Richard. On the Synchronisation Problem over Cellular Automata. 34th Symposium on Theoretical Aspects of Computer Science, STACS 2017, Mar 2017, Hannover, Germany. ⟨10.4230/LIPIcs.STACS.2017.54⟩. ⟨hal-01578448⟩



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