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

  • P. ArrighiEmail author
  • S. Martiel
  • S. Perdrix


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.


Bijective Invertible Injective Surjective One-to-one Onto Cayley graphs Hedlund Block representation Lattice-gas automaton Reversible cellular automata 



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 STICAmSud project 16STIC05 FoQCoSS. The authors acknowledge enlightening discussions with Gilles Dowek, Emmanuel Jeandel and Bruno Martin. This work has been partially done when PA was delegated at Inria Nancy Grand Est, in the project team Carte.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.CNRS, LISAix-Marseille UniversityMarseilleFrance
  2. 2.INRIA, ENS Paris-Saclay, LSVUniversité Paris-SaclayCachanFrance
  3. 3.Atos/Bull, Quantum R&DLes Clayes-sous-BoisFrance
  4. 4.CNRS, LORIA, Inria Project Team CARTEUniv. de LorraineNancyFrance

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