Space-time reversible graph rewriting
Abstract
In the mathematical tradition, reversibility requires that the evolution of a dynamical system be a bijective function. In the context of graph rewriting, however, the evolution is not even a function, because it is not even deterministic -- as the rewrite rules get applied at non-deterministically chosen locations. Physics, by contrast, suggests a more flexible understanding of reversibility in space-time, whereby any two closeby snapshots (aka `space-like cuts'), must mutually determine each other. We build upon the recently developed framework of space-time deterministic graph rewriting, in order to formalise this notion of space-time reversibility, and henceforth study reversible graph rewriting. We establish sufficient, local conditions on the rewrite rules so that they be space-time reversible. We provide an example featuring time dilation, in the spirit of general relativity.
Cite
@article{arxiv.2510.03296,
title = {Space-time reversible graph rewriting},
author = {Pablo Arrighi and Marin Costes and Luidnel Maignan},
journal= {arXiv preprint arXiv:2510.03296},
year = {2025}
}