Reversible Causal Graph Dynamics

TL;DR

This paper introduces Reversible Causal Graph Dynamics, extending Cellular Automata to dynamic, bounded-degree graphs with symmetries like shift-invariance, causality, and reversibility, enabling physics-like modeling of evolving networks.

Contribution

It formalizes reversible dynamics on time-varying graphs, incorporating reversibility as a new symmetry in the framework of Causal Graph Dynamics.

Findings

Defines reversible causal graph dynamics with physics-like symmetries

Establishes conditions for invertibility and reversibility in graph evolution

Provides a mathematical framework for reversible network evolution

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 add a further physics-like symmetry, namely reversibility. KEYWORDS: Bijective, invertible, injective, surjective, one-to-one, onto, Cayley graphs, Hedlund, Block representation, Lattice-gas automaton, Reversible Cellular Automata.