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On the degrees of non-regularity and non-context-freeness
Journal of Computer and System Sciences ( IF 1.1 ) Pub Date : 2019-10-24 , DOI: 10.1016/j.jcss.2019.09.003
Henning Bordihn , Victor Mitrana

We study the derivational complexity of context-free and context-sensitive grammars by counting the maximal number of non-regular and non-context-free rules used in a derivation, respectively. The degree of non-regularity/non-context-freeness of a language is the minimum degree of non-regularity/non-context-freeness of context-free/context-sensitive grammars generating it. A language has finite degree of non-regularity iff it is regular. We give a condition for deciding whether the degree of non-regularity of a given unambiguous context-free grammar is finite. The problem becomes undecidable for arbitrary linear context-free grammars. The degree of non-regularity of unambiguous context-free grammars generating non-regular languages as well as that of grammars generating deterministic context-free languages that are not regular is of order Ω(n). Context-free non-regular languages of sublinear degree of non-regularity are presented. A language has finite degree of non-context-freeness iff it is context-free. Context-sensitive grammars with a quadratic degree of non-context-freeness are more powerful than those of a linear degree.



中文翻译:

关于非规则性和非上下文无关性的程度

通过分别计算派生中使用的非规则和非上下文无关规则的最大数量,我们研究了上下文无关和上下文敏感语法的派生复杂性。语言的非规则性/非上下文无关性程度是生成语言的上下文无关/上下文敏感语法的最小非规则性/非上下文无关性程度。如果语言是规则的,则它具有一定程度的非规则性。我们给出一个条件来确定给定的无上下文无关语法的不规则程度是否是有限的。对于任意线性无上下文无关文法,问题变得无法确定。生成非常规语言的明确上下文无关语法的不规则程度以及生成非常规确定性上下文无关语言的语法的不规则程度是有序的Ωñ。提出了非线性亚非正规度的上下文无关非正规语言。如果语言是上下文无关的,则它具有一定程度的非上下文无关性。具有二次上下文无关性的上下文敏感文法比具有线性程度的上下文敏感文法更强大。

更新日期:2019-10-24
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