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Descriptional Complexity of Unambiguous Nested Word Automata

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Language and Automata Theory and Applications (LATA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6638))

Abstract

It is known that converting an n-state nondeterministic nested word automaton (a.k.a. input-driven automaton; a.k.a. visibly pushdown automaton) to a corresponding deterministic automaton requires in the worst case \(2^{\Theta(n^2)}\) states (R. Alur, P. Madhusudan: Adding nesting structure to words, DLT’06). We show that the same worst case \(2^{\Theta(n^2)}\) size blow-up occurs when converting a nondeterministic nested word automaton to an unambiguous one, and an unambiguous nested word automaton to a deterministic one. In addition, the methods developed in this paper are used to demonstrate that the state complexity of complementation for nondeterministic nested word automata is \(2^{\Theta(n^2)}\), and that the state complexity of homomorphism for deterministic nested word automata is \(2^{\Theta(n^2)}\).

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Author information

Authors and Affiliations

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

    Alexander Okhotin

  2. Academy of Finland, Finland

    Alexander Okhotin

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

    Kai Salomaa

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  1. Alexander Okhotin
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  2. Kai Salomaa
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Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

  2. Department of Informatics, Kyushu University, 744 Motooka, 819–0395, Fukuoka, Japan

    Shunsuke Inenaga

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Okhotin, A., Salomaa, K. (2011). Descriptional Complexity of Unambiguous Nested Word Automata. In: Dediu, AH., Inenaga, S., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2011. Lecture Notes in Computer Science, vol 6638. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21254-3_33

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  • DOI: https://doi.org/10.1007/978-3-642-21254-3_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21253-6

  • Online ISBN: 978-3-642-21254-3

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