Reversible causal graph dynamics: invertibility, block representation, vertex-preservation

Abstract : Causal Graph Dynamics extend Cellular Automata to arbitrary time-varying graphs of bounded degree. The whole graph evolves in discrete time steps, and this global evolution is required to have a number of symmetries: shift-invariance (it acts everywhere the same) and causality (information has a bounded speed of propagation). We add a further physics-like symmetry, namely reversibility. In particular, we extend two fundamental results on reversible cellular automata, by proving that the inverse of a causal graph dynamics is a causal graph dynamics, and that these reversible causal graph dynamics can be represented as finite-depth circuits of local reversible gates. We also show that reversible causal graph dynamics preserve the size of all but a finite number of graphs.
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https://hal.archives-ouvertes.fr/hal-02400095
Contributor : Simon Perdrix <>
Submitted on : Monday, December 9, 2019 - 1:36:16 PM
Last modification on : Monday, January 13, 2020 - 1:18:40 AM

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Pablo Arrighi, Simon Martiel, Simon Perdrix. Reversible causal graph dynamics: invertibility, block representation, vertex-preservation. Natural Computing, Springer Verlag, 2019, ⟨10.1007/s11047-019-09768-0⟩. ⟨hal-02400095⟩

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