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On the Trade-off Between Ambiguity and Complexity in Contextual Languages
Contextual grammars are introduced by Solomon Marcus in 1969 based on the fundamental concept of descriptive linguistics of insertion of strings in given contexts. Internal contextual grammars are introduced by Paun and Nguyen in 1980. For contextual grammars several descriptional complexity measures and levels of ambiguity have been defined. In this paper, we analyze the trade-off between ambiguity and complexity of languages generated by internal contextual grammars. The notion of a pseudo inherently ambiguous language with respect to two complexity mea-
sures is introduced and investigated. These languages can be generated by unambiguous grammars which are minimal with respect to one measure and ambiguous if they are minimal with respect to the other measure. An open problem by Paun in the Marcus Contextual Grammar book is solved in this framework.