10.46298/dmtcs.2973
https://dmtcs.episciences.org/2973
Nesme, Vincent
Vincent
Nesme
Theyssier, Guillaume
Guillaume
Theyssier
Selfsimilarity, Simulation and Spacetime Symmetries
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.
episciences.org
cellular automata
simulation
reversibility
time symmetry
space symmetry
linear
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]
[NLIN.NLIN-CG] Nonlinear Sciences [physics]/Cellular Automata and Lattice Gases [nlin.CG]
[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
2023-04-02
2011-01-01
2011-01-01
en
journal article
https://hal.science/hal-01196140v1
1365-8050
https://dmtcs.episciences.org/2973/pdf
VoR
application/pdf
Discrete Mathematics & Theoretical Computer Science
DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems
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