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

  • Authors:

  • Henning Bordihn;Markus Holzer;Martin Kutrib

  • Affiliations:

  • Institut für Informatik, Universität Potsdam, Potsdam, Germany;Institut für Informatik, Technische Universität München, Garching bei München, Germany;Institut für Informatik, Universität Gießen, Gießen, Germany

  • Venue:
  • DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
  • Year:
  • 2004

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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.