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arXiv · 2609.23567

Contributions to the hierarchy of probabilistic languages

Lothar Sebastian Krapp·Remo Nitschke
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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.

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Lothar Sebastian Krapp, Remo Nitschke. 2026-09-20. Contributions to the hierarchy of probabilistic languages. https://arxiv.org/abs/2609.23567

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