# Does a notion of a context-free complete language exist?

Is there a notion of a context-free complete language (in the analogous sense to a $$NP$$-complete language)?

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Lautemann and Schwentick prove that Greibach's "hardest context-free grammar" with a neutral symbol is complete for $$LOGCFL$$ and hence $$CFL$$ also, under quantifier-free projection without BIT.