On the Complexity of Membership and Counting in Height-Deterministic Pushdown Automata

  • Nutan Limaye
  • Meena Mahajan
  • Antoine Meyer
Conference paper

DOI: 10.1007/978-3-540-79709-8_25

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5010)
Cite this paper as:
Limaye N., Mahajan M., Meyer A. (2008) On the Complexity of Membership and Counting in Height-Deterministic Pushdown Automata. In: Hirsch E.A., Razborov A.A., Semenov A., Slissenko A. (eds) Computer Science – Theory and Applications. CSR 2008. Lecture Notes in Computer Science, vol 5010. Springer, Berlin, Heidelberg

Abstract

While visibly pushdown languages properly generalise regular languages and are properly contained in deterministic context-free languages, the complexity of their membership problem is equivalent to that of regular languages. However, the corresponding counting problem could be harder than counting paths in a non-deterministic finite automaton: it is only known to be in LogDCFL.

We investigate the membership and counting problems for generalisations of visibly pushdown automata, defined using the notion of height-determinism. We show that, when the stack-height of a given PDA can be computed using a finite transducer, both problems have the same complexity as for visibly pushdown languages. We also show that when allowing pushdown transducers instead of finite-state ones, both problems become LogDCFL-complete; this uses the fact that pushdown transducers are sufficient to compute the stack heights of all real-time height-deterministic pushdown automata, and yields a candidate arithmetization of LogDCFL that is no harder than LogDCFL(our main result).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Nutan Limaye
    • 1
  • Meena Mahajan
    • 1
  • Antoine Meyer
    • 2
  1. 1.The Institute of Mathematical SciencesChennaiIndia
  2. 2.LIAFAUniversité Paris Diderot – Paris 7Paris Cedex 13France

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