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Non-Self-Embedding Grammars, Constant-Height Pushdown Automata, and Limited Automata
International Journal of Foundations of Computer Science ( IF 0.6 ) Pub Date : 2020-12-29 , DOI: 10.1142/s0129054120420071
Bruno Guillon 1 , Giovanni Pighizzini 2 , Luca Prigioniero 2
Affiliation  

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.

中文翻译:

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。
更新日期:2020-12-29
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