Reversible Causal Graph Dynamics
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.
KeywordsBijective Invertible Cayley graphs Hedlund 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 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.
- 2.Arrighi, P., Martiel, S., Nesme, V., Cayley, G.: Graphs, cellular automata over them submitted (long version) (2013). Pre-print arXiv:1212.0027
- 11.Hasslacher, B., Meyer, D.A.: Modelling dynamical geometry with lattice gas automata. In: Expanded Version of a Talk Presented at the Seventh International Conference on the Discrete Simulation of Fluids Held at the University of Oxford, June 1998Google Scholar
- 13.Kari, J.: Reversibility of 2D cellular automata is undecidable. In: Cellular Automata: Theory and Experiment, vol. 45, pp. 379–385. MIT Press (1991)Google Scholar
- 17.Konopka, T., Markopoulou, F., Smolin, L.: Quantum graphity. Arxiv preprint arXiv:hep-th/0611197 (2006)
- 20.Taentzer, G.: Parallel and distributed graph transformation: formal description and application to communication-based systems. Ph.D. thesis, Technische Universitat Berlin (1996)Google Scholar