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Contributions to the hierarchy of probabilistic languages — arXiv:2609.23567

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.23567
License (as archived): CC0-1.0
Archived: 2026-10-09T06:50:36.610Z
SHA-256 of the archived text: d3e2ffb2953cc0210193f93da3e6bd6f7c6ddf3f5e02f2ddd0619dff6f2e51ce
Stable URL of this page: https://metraipolis.com/documento/dc_eb4d47809eeb

How to cite

Contributions to the hierarchy of probabilistic languages — arXiv:2609.23567 — arXiv (en), https://arxiv.org/abs/2609.23567 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_eb4d47809eeb (Metraipolis archive dc_eb4d47809eeb, sha256 d3e2ffb2953cc0210193f93da3e6bd6f7c6ddf3f5e02f2ddd0619dff6f2e51ce)

BibTeX

@misc{dceb4d47809eeb,
  title = {Contributions to the hierarchy of probabilistic languages — arXiv:2609.23567},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.23567},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_eb4d47809eeb; sha256 d3e2ffb2953cc0210193f93da3e6bd6f7c6ddf3f5e02f2ddd0619dff6f2e51ce},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.23567. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-22 in cs.CL).
Categorie arXiv: Formal Languages and Automata Theory (cs.FL) ; Computation and Language (cs.CL); Logic (math.LO); Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.23567 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T06:48:45.127Z dalla pagina https://arxiv.org/catchup/cs.CL/2026-09-22?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).