Degrees of nondeterminism for pushdown automata

Abstract

Savitch and Vermeir in [7] introduced two measures for nondeterminism of pushdown automata and showed interestingly that the second measure yields an infinite hierarchy of language families between the deterministic context-free and general context-free languages. However, the proof given in [7] for this hierarchy theorem was incorrect. In this paper, we show that all the languages used in [7] to separate different families of the hierarchy actually belong to the first level above the DCFLs. We give a new proof for the hierarchy theorem. We also introduce a new and intuitive measure for nondeterminism and show that it is equivalent to Savitch and Vermeir’s second measure.