Context-free grammars are not able to capture cross-serial dependencies occurring in some natural languages. To overcome this issue, Seki et al. introduced a generalization called m-multiple context-free grammars (m-MCFGs), which deal with m-tuples of strings. We show that m-MCFGs are capable of comparing the number of consecutive occurrences of at most 2m different letters. In particular, the language $\{a_1^{n_1}{a}_2^{n_2}\cdots a_{2m+1}^{n_{2m+1}}|n_1\ge n_2\ge \dots \ge n_{2m+1}\ge 0\}$ is $(m+1)$-multiple context-free, but not m-multiple context-free.

中文翻译：

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比较多种上下文无关语言中的连续字母计数

上下文无关的语法无法捕获某些自然语言中出现的跨序列依赖项。为了克服这个问题，Seki等人。引入了一个称为m的多上下文无关文法（m -MCFGs）的概括，它处理字符串的m个元组。我们显示m -MCFGs能够比较最多2 m个不同字母的连续出现次数。特别是语言$\{{\mathrm{一种}}_{\mathrm{1个}}^{{ñ}_{\mathrm{1个}}}{\mathrm{一种}}_{\mathrm{2个}}^{{ñ}_{\mathrm{2个}}}\cdots {\mathrm{一种}}_{\mathrm{2个}米+\mathrm{1个}}^{{ñ}_{\mathrm{2个}米+\mathrm{1个}}}|{ñ}_{\mathrm{1个}}\ge {ñ}_{\mathrm{2个}}\ge \dots \ge {ñ}_{\mathrm{2个}米+\mathrm{1个}}\ge 0\}$ 是 $（米+\mathrm{1个}）$-多个上下文无关，但不是m-多个上下文无关。