Vincent Nesme ; Guillaume Theyssier

Selfsimilarity, Simulation and Spacetime Symmetries
dmtcs:2973 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2011,
DMTCS Proceedings vol. AP, Automata 2011  17th International Workshop on Cellular Automata and Discrete Complex Systems

https://doi.org/10.46298/dmtcs.2973
Selfsimilarity, Simulation and Spacetime Symmetries
Authors: Vincent Nesme ^{1}; Guillaume Theyssier ^{2}
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Vincent Nesme;Guillaume Theyssier
1 Freie Universität Berlin
2 Laboratoire de Mathématiques
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 spacetime diagrams generated from finite configurations. As an illustration, we give an example of linear reversible CA which cannot simulate the identity and which is 'timeasymmetric', i.e. which can neither simulate its own inverse, nor the mirror of its own inverse.