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A useful lemma for context-free programmed grammars

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Abstract

We show that all quasi-realtime one-way multi-counter languages can be generated by a context-free ɛ-free programmed grammar (even under the free interpretation). The result can be used to obtain a new and almost trivial proof of the fundamental theorem that arbitrary context-free programmed grammars can generate all recursively enumerable languages. The proof of our result also yields the following, interesting characterization: the quasi-realtime one-way multi-counter languages are precisely the ɛ-limited homomorphic images of (free) context-free programmed production languages. It follows that the (free) derivation languages of context-free or even context-free programmed grammars, which were known to be context-sensitive, are in fact contained in the family of context-free ɛ-free programmed languages.

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  1. Department of Computer Science, University of Utrecht, P.O. Box 80.012, 3508, TA Utrecht, The Netherlands

    Jan van Leeuwen

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  1. Jan van Leeuwen
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van Leeuwen, J. A useful lemma for context-free programmed grammars. Acta Informatica 11, 373–386 (1979). https://doi.org/10.1007/BF00289095

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  • DOI: https://doi.org/10.1007/BF00289095

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