Comments on universal and left universal grammars, context-sensitive languages, and context-free grammar forms

S.A Greibach

doi:10.1016/s0019-9958(78)90799-4

S.A Greibach

https://doi.org/10.1016/s0019-9958(78)90799-4

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Journal: Information and Control	Publication Date: Nov 1, 1978
Citations: 10	License type: elsevier-specific: oa user license

Affiliation: University of California, Los Angeles

Abstract

A grammar G is left universal (universal) for a family of languages ℒ and finite alphabet Σ with respect to a family of languages ℒ 1 , if ℒ restricted to subsets of Σ * is the family of subsets of Σ * obtained by using members of ℒ 1 to control left-to-right derivations (unrestricted derivations) of G ; if ℒ 1 is the family of regular sets, G is called simply left universal or universal for ℒ and Σ . There is no context-sensitive grammar universal for the class of context-sensitive languages even over a one-letter alphabet. There is a context-free grammar which is left universal for the class of recursively enumerable languages with respect to the family of linear context-free languages. There is a linear context-free grammar which is universal and left universal for the family of linear contextfree languages. If G is a nontrivial left-derivation-bounded context-free grammar, then for each finite alphabet Σ there is a left-derivation-bounded contextfree grammar which is left universal for ℒ and Σ , where ℒ is the family of languages generated by interpretations of G as a context-free grammar form.

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