Selfsimilarity, Simulation and Spacetime Symmetries

Abstract : We study intrinsic simulations between cellular automata and introduce a new necessary condition for a CA to simulate another one. Although expressed for general CA, this condition is targeted towards surjective CA and especially linear ones. Following the approach introduced by the first author in an earlier paper, we develop proof techniques to tell whether some linear CA can simulate another linear CA. Besides rigorous proofs, the necessary condition for the simulation to occur can be heuristically checked via simple observations of typical space-time diagrams generated from finite configurations. As an illustration, we give an example of linear reversible CA which cannot simulate the identity and which is 'time-asymmetric', i.e. which can neither simulate its own inverse, nor the mirror of its own inverse.
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Pré-publication, Document de travail
2011
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https://hal.archives-ouvertes.fr/hal-00649749
Contributeur : Guillaume Theyssier <>
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Dernière modification le : jeudi 11 janvier 2018 - 06:12:26
Document(s) archivé(s) le : vendredi 16 novembre 2012 - 14:55:37

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  • HAL Id : hal-00649749, version 1
  • ARXIV : 1112.1933

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Vincent Nesme, Guillaume Theyssier. Selfsimilarity, Simulation and Spacetime Symmetries. 2011. 〈hal-00649749〉

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