{
  "abstract": "Let $G$ be a group, let $\\mathbb{K}$ be a field, and let $V$ be a $\\mathbb{K}$-vector space. We prove that there exists a bijective linear cellular automaton $V^G\\to V^G$ whose inverse is not a cellular automaton if and only if $G$ is not locally finite and $\\dim_{\\mathbb{K}}V \\geq |\\mathbb{K}|^{\\aleph_0}$. In particular, $|\\mathbb{K}|^{\\aleph_0}$ is the exact dimension threshold for non-reversibility. This answers an open problem proposed by T. Ceccherini-Silberstein and M. Coornaert.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.20600",
  "author_total": 1,
  "authors": [
    {
      "name": "Alonso Castillo-Ramirez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9srfpn8m1vtqb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.20600",
  "fulltext_url": null,
  "id": "9srfpn8m1vtqb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.20600",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.FL"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "1703|Cellular Automata and Applications"
    ]
  ],
  "openalex": "W7204123502",
  "pdf_url": "https://arxiv.org/pdf/2608.20600",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9srfpn8m1vtqb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2608.20600",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.20600"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "A characterization of the reversibility of linear cellular automata",
  "title_text": "A characterization of the reversibility of linear cellular automata",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/9srfpn8m1vtqb",
  "venue": "arXiv",
  "versions": []
}