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| | formallangfibres |
 | | For type-2 languages, a theorem of Greibach states the existence of a universal such, i.e., a context-free language L_{gr} such that every other context-free language is a homomorphic pre-image of L_{gr}. |
 | | ([HK] has a construction of L_{gr} over a 7-element alphabet, but then one can of course find another such universal context-free language over a 2-element alphabet.) References: [G] Sheila A. Greibach: The hardest context-free language. |
 | | Standard results of formal language theory tell us that for i\in\{0,2,3\} the restriction of U to lang_i still is a bi-fibration, while the restriction of U to lang_1 still is a fibration, but not a cofibration, since homomorphic images of type-1 languages need not be of type 1. |
| www.mta.ca /~cat-dist/catlist/1999/formallangfibres (335 words) |
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