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Hankel Matrices for Weighted Visibly Pushdown Automata

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Language and Automata Theory and Applications (LATA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9618))

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Abstract

Hankel matrices (aka connection matrices) of word functions and graph parameters have wide applications in automata theory, graph theory, and machine learning. We give a characterization of real-valued functions on nested words recognized by weighted visibly pushdown automata in terms of Hankel matrices on nested words. This complements C. Mathissen’s characterization in terms of weighted monadic second order logic.

Nadia Labai—Supported by the National Research Network RiSE (S114), and the LogiCS doctoral program (W1255) funded by the Austrian Science Fund (FWF).

Johann A. Makowsky—Partially supported by a grant of Technion Research Authority.

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Notes

  1. 1.

    This formalism was originally introduced in [18] for graph parameters.

  2. 2.

    The original definition of nested words allowed “dangling” edges. We will only be concerned with nested words that are well-matched.

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Acknowledgments

We thank Boaz Blankrot for helpful discussions on matrix decompositions and the anonymous referees for valuable feedback.

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Authors and Affiliations

  1. Department of Informatics, Vienna University of Technology, Vienna, Austria

    Nadia Labai

  2. Department of Computer Science, Technion - Israel Institute of Technology, Haifa, Israel

    Johann A. Makowsky

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  1. Nadia Labai
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Correspondence to Nadia Labai .

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Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Spain

    Adrian-Horia Dediu

  2. Czech Technical University, Prague, Czech Republic

    Jan Janoušek

  3. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  4. Justus Liebig University Giessen, Gießen, Germany

    Bianca Truthe

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Labai, N., Makowsky, J.A. (2016). Hankel Matrices for Weighted Visibly Pushdown Automata. In: Dediu, AH., Janoušek, J., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2016. Lecture Notes in Computer Science(), vol 9618. Springer, Cham. https://doi.org/10.1007/978-3-319-30000-9_36

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