Remarks on the Cellular Automaton Global Synchronisation Problem

Nazim Fatès 1
1 MAIA - Autonomous intelligent machine
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The global synchronisation problem consists in making a cellular automaton converge to a homogeneous blinking state from any initial condition. We here study this inverse problem for one-dimensional binary systems with periodic boundary conditions (i.e., rings). For small neighbourhoods, we present results obtained with the formulation of the problem as a SAT problem and the use of SAT solvers. Our observations suggest that it is not possible to solve this problem perfectly with deterministic systems. In contrast, the problem can easily be solved with stochastic rules.
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Nazim Fatès. Remarks on the Cellular Automaton Global Synchronisation Problem. 21st Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jarkko Kari, Jun 2015, Turku, Finland. pp.113-126, ⟨10.1007/978-3-662-47221-7_9⟩. ⟨hal-01255925⟩

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