Abstract
We define a complexity measure on context-free grammars called end. Roughly speaking, for a context-free grammar G, endG(n) measures the distance of variables from the ends of sentential forms along the derivations of words in L(G) of length n. We prove in a constructive way the regularity of L(G)wheneverendG(n)is constant. Yet, we improve on this by showing that ifL(G)is nonregular thenendG(n) = Ω∞( log n). We establish the optimality of such bound. Finally, we show that, in case of unambiguous context-free grammars, the end lower bound for generating nonregular languages turns out to be linear.
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