{
  "abstract": "We introduce causal graph rewriting, a model of computation in which local rules are applied on directed acyclic graphs in an asynchronous manner. The non-determinism arising from asynchrony is disciplined by the oriented edges, which must be understood as both computational dependencies and locality constraints---and are themselves subject to the rewriting. We illustrate the model through two examples: a particle system, and a time-dilation example---reminiscent of general relativity. We study the well-definedness and properties of induced subgraphs and graph composition, which isolate and recombine the region affected by a rewrite. We then study locality with respect to these constructions, showing how a local rewrite preserves positions, borders, and context. Our main result concerns sequential composition: locality extends from single rule applications to arbitrary valid sequences, as any local rule is automatically $*$-local and $*$-extensive. We also formalise and prove the simulation of any one-dimensional cellular automaton.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25188",
  "author_total": 3,
  "authors": [
    {
      "name": "Pablo Arrighi"
    },
    {
      "name": "Marin Costes"
    },
    {
      "name": "Luidnel Maignan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c3jn6qranjgym.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25188",
  "fulltext_url": null,
  "id": "c3jn6qranjgym",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25188",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.FL"
    ],
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      "arxiv",
      "math-ph"
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      "arxiv",
      "math.DS"
    ],
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      "arxiv",
      "math.MP"
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      "arxiv",
      "nlin.CG"
    ],
    [
      "openalex",
      "1703|Cellular Automata and Applications"
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  ],
  "openalex": "W7214088731",
  "pdf_url": "https://arxiv.org/pdf/2609.25188",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c3jn6qranjgym.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.25188",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25188"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.CG",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Causal graph rewriting",
  "title_text": "Causal graph rewriting",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/c3jn6qranjgym",
  "venue": "arXiv",
  "versions": []
}