A Parallel Context-Free Derivation Hierarchy

Authors:
Klaus Reinhardt
Affiliations:
-
Venue:
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
Year:
1999

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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.