对概率语言层级结构的贡献
Contributions to the hierarchy of probabilistic languages
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- Universität Zürich（苏黎世大学）
- Universität Konstanz（康斯坦茨大学）
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中文总结 AI 辅助
本文证明n-gram模型生成的概率语言均可用PCFG生成，但反之不然；引入全连接PCFG，证明n-gram语言类并非全连接PCFG语言类的子集。
中文摘要 AI 辅助
我们重新审视由n-gram模型和概率上下文无关文法（PCFGs）生成的概率形式语言理论。通过证明每个由n-gram模型生成的概率语言也由某个PCFG生成，而某些由PCFG生成的概率语言不能被任何n-gram模型生成，从而确立了预期的概率文法层级结构。我们引入了全连接PCFG的概念，即乔姆斯基范式中的PCFG，其中每个仅涉及非终结符的产生规则具有非零概率。我们的主要结果表明，任何由n-gram模型生成的概率语言与任何由全连接PCFG生成的概率语言不同。因此，由n-gram模型生成的概率语言类不是由全连接PCFG生成的类的子集。
英文摘要
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.
