Non-self-embedding grammars are a subclass of context-free grammars which only generate regular languages. The size costs of the conversion of non-self-embedding grammars into equivalent finite automata are studied, by proving optimal bounds for the number of states of nondeterministic and deterministic automata equivalent to given non-self-embedding grammars. In particular, each non-self-embedding grammar of size s can be converted into an equivalent nondeterministic automaton which has an exponential size in s and into an equivalent deterministic automaton which has a double exponential size in s. These costs are shown to be optimal. Moreover, they do not change if the larger class of quasi-non-self-embedding grammars, which still generate only regular languages, is considered. In the case of letter bounded languages, the cost of the conversion of non-self-embedding grammars and quasi-non-self-embedding grammars into deterministic automata reduces to an exponential of a polynomial in s.

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非自嵌入语法和描述复杂性

非自嵌入语法是无上下文语法的子类，仅生成常规语言。通过证明非确定性和确定性自动机的等价于给定非自我嵌入语法的状态数的最优界限，研究了将非自我嵌入语法转换为等效有限自动机的大小成本。特别地，大小为s的每个非自嵌入语法都可以转换为s的指数大小的等效非确定性自动机，以及为s的双指数大小的等效确定性自动机。这些成本被证明是最佳的。此外，如果考虑仍仅生成常规语言的较大类的非自嵌入语法，则它们不会改变。对于字母限制语言，