Constant Acceleration Theorem for Extended von Neumann Neighbourhoods

Anaël Grandjean 1
1 ESCAPE - Systèmes complexes, automates et pavages
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We study 2-dimensional cellular automata as language recog-nizers. We are looking for closure properties, similar to the one existing in one dimension. Some results are already known for the most used neighbourhoods, however many problems remain open concerning more general neighbourhoods. In this paper we provide a construction to prove a constant acceleration theorem for extended von Neumann neighbourhoods. We then use this theorem and some classical tools to prove the equivalence of those neighbourhoods, considering the set of languages recognizable in real time.
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Communication dans un congrès
Matthew Cook; Turlough Neary. 22th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2016, Zurich, Switzerland. Springer, Lecture Notes in Computer Science, LNCS-9664, pp.149-158, 2016, Cellular Automata and Discrete Complex Systems. 〈10.1007/978-3-319-39300-1_12〉
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Anaël Grandjean. Constant Acceleration Theorem for Extended von Neumann Neighbourhoods. Matthew Cook; Turlough Neary. 22th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2016, Zurich, Switzerland. Springer, Lecture Notes in Computer Science, LNCS-9664, pp.149-158, 2016, Cellular Automata and Discrete Complex Systems. 〈10.1007/978-3-319-39300-1_12〉. 〈lirmm-01476307〉

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