{
  "abstract": "We reconsider the theory of probabilistic formal languages generated by n-gram models and by probabilistic context-free grammars (PCFGs). The expected hierarchy of probabilistic grammars is established by proving that every probabilistic language generated by an n-gram model is also generated by some PCFG, while some probabilistic languages generated by PCFGs cannot be generated by any $n$-gram model. We introduce the notion of fully connected PCFGs, namely PCFGs in Chomsky normal form where every production rule only involving non-terminals has non-zero probability. Our main result shows that any probabilistic language generated by an $n$-gram model differs from any probabilistic language generated by a fully connected PCFG. Therefore, the class of probabilistic languages generated by $n$-gram models is not a subset of the class generated by fully connected PCFGs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23567",
  "author_total": 2,
  "authors": [
    {
      "name": "Lothar Sebastian Krapp"
    },
    {
      "name": "Remo Nitschke"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e7rbmvmbrfrea.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23567",
  "fulltext_url": null,
  "id": "e7rbmvmbrfrea",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23567",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CL"
    ],
    [
      "arxiv",
      "cs.FL"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
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      "openalex",
      "1703|semigroups and automata theory"
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  ],
  "openalex": "W7214034486",
  "pdf_url": "https://arxiv.org/pdf/2609.23567",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e7rbmvmbrfrea.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23567",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23567"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Contributions to the hierarchy of probabilistic languages",
  "title_text": "Contributions to the hierarchy of probabilistic languages",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/e7rbmvmbrfrea",
  "venue": "arXiv",
  "versions": []
}