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On the degrees of non-regularity and non-context-freeness
Journal of Computer and System Sciences ( IF 1.129 ) 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.
更新日期:2020-01-04

 

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