{
  "abstract": "In this paper we show that for each small permutation class $\\mathcal{F}$ there exists a regular language $L_\\mathcal{F}$ such that the monadic second-order TOTO logic on $\\mathcal{F}$ is isomorphic to classical monadic second-order logic on $L_\\mathcal{F}$. Thanks to the fact that regular languages are closed under monadic second-order restrictions this shows that many subsets of $\\mathcal{F}$ have a well-behaved structure. In particular, this allows us to show that random permutations from any small permutation class satisfies convergence laws for both first-order logic and monadic second-order logic. In the latter case, the law is modular. Our proofs introduce a way of using the automaton description of regular languages to prove properties of generating functions which may be of independent interest. Potential applications include first-order limit laws for random words in some regular languages.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22218",
  "author_total": 2,
  "authors": [
    {
      "name": "Klas Markström"
    },
    {
      "name": "Eero Räty"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/42ehjazhecd0z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22218",
  "fulltext_url": null,
  "id": "42ehjazhecd0z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22218",
  "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",
      "math.CO"
    ],
    [
      "openalex",
      "1703|semigroups and automata theory"
    ]
  ],
  "openalex": "W7222691226",
  "pdf_url": "https://arxiv.org/pdf/2610.22218",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/42ehjazhecd0z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.22218",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22218"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Logical isomorphism and logical limit laws for small permutation classes and regular languages",
  "title_text": "Logical isomorphism and logical limit laws for small permutation classes and regular languages",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/42ehjazhecd0z",
  "venue": "arXiv",
  "versions": []
}