Contributions to the hierarchy of probabilistic languages

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.

Formal Languages and Automata Theory (cs.FL); Computation and Language (cs.CL); Logic (math.LO); Probability (math.PR)

arXiv:2609.23567 [cs.FL]

(or arXiv:2609.23567v1 [cs.FL] for this version)

https://doi.org/10.48550/arXiv.2609.23567 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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