Space-time reversible graph rewriting
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918153983885312 |
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| author | Arrighi, Pablo Costes, Marin Maignan, Luidnel |
| author_facet | Arrighi, Pablo Costes, Marin Maignan, Luidnel |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_03296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Space-time reversible graph rewriting Arrighi, Pablo Costes, Marin Maignan, Luidnel Discrete Mathematics Mathematical Physics 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. |
| title | Space-time reversible graph rewriting |
| topic | Discrete Mathematics Mathematical Physics |
| url | https://arxiv.org/abs/2510.03296 |