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Descriptional Complexity of Input-Driven Pushdown Automata

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Languages Alive

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7300))

Abstract

It is known that a nondeterministic input-driven pushdown automaton (IDPDA) can be determinized. Alur and Madhusudan (“Adding nesting structure to words”, J.ACM 56(3), 2009) showed that a deterministic IDPDA simulating a nondeterministic IDPDA with n states and stack symbols may need, in the worst case, \(2^{\Omega(n^2)}\) states. In their construction, the equivalent deterministic IDPDA does, in fact, not need to use the stack. This paper considers the size blow-up of determinization in more detail, and gives a lower bound construction, that is tight within a multiplicative constant, with respect to the size of the nondeterministic automaton both for the number of states and the number of stack symbols. The paper also surveys the recent results on operational state complexity of IDPDAs, and on the cost of converting a nondeterministic automaton to an unambiguous one, and an unambiguous automaton to a deterministic one.

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Authors and Affiliations

  1. Department of Mathematics, University of Turku, 20014, Turku, Finland

    Alexander Okhotin

  2. School of Computing, Queen’s University, Kingston, Ontario, K7L 3N6, Canada

    Xiaoxue Piao & Kai Salomaa

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  1. Alexander Okhotin
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  2. Xiaoxue Piao
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  3. Kai Salomaa
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Editors and Affiliations

  1. Institut für Informatik, Universität Potsdam, August-Bebel-Straße 89, 14482, Potsdam, Germany

    Henning Bordihn

  2. Institut für Informatik, Universität Giessen, Arndtstraße 2, 35392, Giessen, Germany

    Martin Kutrib

  3. Fakultät für Informatik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39016, Magdeburg, Germany

    Bianca Truthe

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Okhotin, A., Piao, X., Salomaa, K. (2012). Descriptional Complexity of Input-Driven Pushdown Automata. In: Bordihn, H., Kutrib, M., Truthe, B. (eds) Languages Alive. Lecture Notes in Computer Science, vol 7300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31644-9_13

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  • DOI: https://doi.org/10.1007/978-3-642-31644-9_13

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