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Reversible Causal Graph Dynamics

  • Pablo Arrighi
  • Simon Martiel
  • Simon Perdrix
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9720)

Abstract

Causal Graph Dynamics extend Cellular Automata to arbitrary, bounded-degree, time-varying graphs. The whole graph evolves in discrete time steps, and this global evolution is required to have a number of physics-like symmetries: shift-invariance (it acts everywhere the same) and causality (information has a bounded speed of propagation). We study a further physics-like symmetry, namely reversibility. We extend a fundamental result on reversible cellular automata by proving that the inverse of a causal graph dynamics is a causal graph dynamics. We also address the question of the evolution of the structure of the graphs under reversible causal graph dynamics, showing that any reversible causal graph dynamics preserves the size of all but a finite number of graphs.

Keywords

Bijective Invertible Cayley graphs Hedlund Reversible cellular automata 

Notes

Acknowledgements

This work has been funded by the ANR-12-BS02-007-01 TARMAC grant, the ANR-10-JCJC-0208 CausaQ grant, and the John Templeton Foundation, grant ID 15619. The authors acknowledge enlightening discussions with Bruno Martin and Emmanuel Jeandel. This work has been partially done when PA was delegated at Inria Nancy Grand Est, in the project team Carte.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Aix-Marseille University, LIFMarseille Cedex 9France
  2. 2.University Nice Sophia Antipolis, I3SSophia AntipolisFrance
  3. 3.CNRS, LORIA, Inria Project Team CARTEUniversity de LorraineNancyFrance

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