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

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Computer Science – Theory and Applications (CSR 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5010))

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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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Authors and Affiliations

  1. The Institute of Mathematical Sciences, Chennai, 600 113, India

    Nutan Limaye & Meena Mahajan

  2. LIAFA, Université Paris Diderot – Paris 7, Case 7014, 75205, Paris Cedex 13, France

    Antoine Meyer

Authors
  1. Nutan Limaye
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  2. Meena Mahajan
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  3. Antoine Meyer
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Edward A. Hirsch Alexander A. Razborov Alexei Semenov Anatol Slissenko

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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. https://doi.org/10.1007/978-3-540-79709-8_25

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  • DOI: https://doi.org/10.1007/978-3-540-79709-8_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79708-1

  • Online ISBN: 978-3-540-79709-8

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