Block Representation of 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. More precisely, we show that Reversible Causal Graph Dynamics can be represented as finite-depth circuits of local reversible gates.

[1]  R. Sorkin.  Time-evolution problem in regge calculus , 1975 .

[2]  Hartmut Ehrig,et al.  Parallel and Distributed Derivations in the Single-Pushout Approach , 1993, Theor. Comput. Sci..

[3]  K. Tomita,et al.  Graph automata: natural expression of self-reproduction , 2002 .

[4]  Gabriele Taentzer,et al.  Parallel High-Level Replacement Systems , 1997, Theor. Comput. Sci..

[5]  Gilles Dowek,et al.  Causal Graph Dynamics , 2012, ICALP.

[6]  Jarkko Kari,et al.  On the Circuit Depth of Structurally Reversible Cellular Automata , 1999, Fundam. Informaticae.

[7]  Pablo Arrighi,et al.  Partitioned quantum cellular automata are intrinsically universal , 2010, Natural Computing.

[8]  Vincent Nesme,et al.  Unitarity plus causality implies localizability , 2007, J. Comput. Syst. Sci..

[9]  G. A. Hedlund.  Endomorphisms and automorphisms of the shift dynamical system , 1969, Mathematical systems theory.

[10]  J. Kari.  Representation of reversible cellular automata with block permutations , 1996, Mathematical systems theory.

[11]  Annegret Habel,et al.  Amalgamation of Graph Transformations: A Synchronization Mechanism , 1987, J. Comput. Syst. Sci..

[12]  Simon Perdrix,et al.  Reversible Causal Graph Dynamics , 2015, RC.

[13]  Jérôme Olivier Durand-Lose,et al.  Representing Reversible Cellular Automata with Reversible Block Cellular Automata , 2001, DM-CCG.

[14]  Kenichi Morita,et al.  Computation-Universality of One-Dimensional One-Way Reversible Cellular Automata , 1992, Inf. Process. Lett..