Non-self-embedding grammars are a restriction of context-free grammars which does not allow to describe recursive structures and, hence, which characterizes only the class of regular languages. A double exponential gap in size from non-self-embedding grammars to deterministic finite automata is known. The same size gap is also known from constant-height pushdown automata and [Formula: see text]-limited automata to deterministic finite automata. Constant-height pushdown automata and [Formula: see text]-limited automata are compared with non-self-embedding grammars. It is proved that non-self-embedding grammars and constant-height pushdown automata are polynomially related in size. Furthermore, a polynomial size simulation by [Formula: see text]-limited automata is presented. However, the converse transformation is proved to cost exponential. Finally, a different simulation shows that also the conversion of deterministic constant-height pushdown automata into deterministic [Formula: see text]-limited automata costs polynomial.

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非自嵌入语法、等高下推自动机和有限自动机

非自嵌入文法是对上下文无关文法的限制，它不允许描述递归结构，因此，它只描述了常规语言的类别。已知从非自嵌入语法到确定性有限自动机的大小存在双指数差距。从恒定高度下推自动机和 [公式：见文本] 限制自动机到确定性有限自动机也知道相同大小的差距。将恒定高度下推自动机和 [公式：见正文] 限制自动机与非自嵌入文法进行比较。证明了非自嵌入文法和等高下推自动机在大小上是多项式相关的。此外，提出了由[公式：见文本]限制自动机进行的多项式大小模拟。然而，逆变换被证明是指数级的。