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arXiv · 2510.03296

Space-time reversible graph rewriting

Pablo Arrighi·Marin Costes·Luidnel Maignan
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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.

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Pablo Arrighi, Marin Costes, Luidnel Maignan. 2025-09-29. Space-time reversible graph rewriting. https://arxiv.org/abs/2510.03296

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