Abstract
We consider the minimal height of a derivation tree as a complexity measure for context-free languages and show that this leads to a strict and dense hierarchy between logarithmic and linear (arbitrary) tree height. In doing so, we improve a result obtained by Gabarro in [7]. Furthermore, we provide a counter-example to disprove a conjecture of Čulik and Maurer in [6] who suggested that all languages with logarithmic tree height would be regular. As a new method, we use counter-representations where the successor relation can be handled as the complement of context-free languages. A similar hierarchy is obtained considering the ambiguity as a complexity measure.
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