Input reversals and iterated pushdown automata: A new characterization of khabbaz geometric hierarchy of languages

Abstract

Input-reversal pushdown automata are pushdown automata with the additional power to reverse the unread part of the input. We show that these machines characterize the family of linear context-free indexed languages, and that k + 1 input reversals are better than k for both deterministic and nondeterministic input-reversal pushdown automata, i.e., there are languages which can be recognized by a deterministic input-reversal pushdown automaton with k + 1 input reversals but which cannot be recognized with k input reversals (deterministic or nondeterministic). In passing, input-reversal finite automata are investigated. Moreover, an inherent relation between input-reversal pushdown automata and controlled linear context-free languages are shown, leading to an alternative description of Khabbaz geometric hierarchy of languages by input-reversal iterated pushdown automata. Finally, some computational complexity problems for the investigated language families are considered. © Springer-Verlag Berlin Heidelberg 2004.