Motivated by recent connections to factorised databases, we analyse the efficiency of representations by context free grammars (CFGs). Concretely, we prove a recent conjecture by Kimelfeld, Martens, and Niewerth (ICDT 2025), that for finite languages representations by general CFGs can be doubly-exponentially smaller than those by unambiguous CFGs. To do so, we show the first exponential lower bounds for representation by unambiguous CFGs of a finite language that can efficiently be represented by CFGs. Our proof first reduces the problem to proving a lower bound in a non-standard model of communication complexity. Then, we argue similarly in spirit to a recent discrepancy argument to show the required communication complexity lower bound. Our result also shows that for finite languages nondeterministic finite automata may be exponentially smaller than unambiguous CFGs.

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