A parallel context-free derivation hierarchy

Abstract

We consider the number of parallel derivation steps as complexity measure for context-free languages and show that a strict and dense hierarchy is obtained between logarithmic and linear (arbitrary) tree height. We hereby improve a result of Gabarro. Furthermore we give a non-regular language with logarithmic tree height disproving a conjecture of Culik and Maurer. As a new method we use counter- representations, where the successor relation can be handled as the complement of context-free languages.