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Hankel Matrices: From Words to Graphs (Extended Abstract)

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Language and Automata Theory and Applications (LATA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8977))

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Abstract

We survey recent work on the use of Hankel matrices \(H(f, \Box )\) for real-valued graph parameters \(f\) and a binary sum-like operation \(\Box \) on labeled graphs such as the disjoint union and various gluing operations of pairs of laeled graphs. Special cases deal with real-valued word functions. We start with graph parameters definable in Monadic Second Order Logic \(\mathrm {MSOL}\) and show how \(\mathrm {MSOL}\)-definability can be replaced by the assumption that \(H(f, \Box )\) has finite rank. In contrast to \(\mathrm {MSOL}\)-definable graph parameters, there are uncountably many graph parameters \(f\) with Hankel matrices of finite rank. We also discuss how real-valued graph parameters can be replaced by graph parameters with values in commutative semirings.

J.A. Makowsky: Partially supported by a grant of Technion Research Authority.

N. Labai: Partially supported by a grant of the Graduate School of the Technion.

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Authors and Affiliations

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

    Johann A. Makowsky & Nadia Labai

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  1. Johann A. Makowsky
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  2. Nadia Labai
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Correspondence to Johann A. Makowsky .

Editor information

Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Spain

    Adrian-Horia Dediu

  2. Nice Sophia Antipolis University, Sophia Antipolis, France

    Enrico Formenti

  3. Mathematical Linguistics, Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  4. Justus-Liebig-Universität, Gießen, Germany

    Bianca Truthe

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Makowsky, J.A., Labai, N. (2015). Hankel Matrices: From Words to Graphs (Extended Abstract). In: Dediu, AH., Formenti, E., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2015. Lecture Notes in Computer Science(), vol 8977. Springer, Cham. https://doi.org/10.1007/978-3-319-15579-1_3

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  • DOI: https://doi.org/10.1007/978-3-319-15579-1_3

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