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

  • Nutan Limaye
  • Meena Mahajan
  • Antoine Meyer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5010)


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).


Regular Language Height Function Language Class Input Word Counting Problem 
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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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