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International Colloquium on Automata, Languages, and Programming

ICALP 2008: Automata, Languages and Programming pp 221–232Cite as

Weighted Logics for Nested Words and Algebraic Formal Power Series

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5126))

Abstract

Nested words, a model for recursive programs proposed by Alur and Madhusudan, have recently gained much interest. In this paper we introduce quantitative extensions and study nested word series which assign to nested words elements of a semiring. We show that regular nested word series coincide with series definable in weighted logics as introduced by Droste and Gastin. For this, we establish a connection between nested words and series-parallel-biposets. Applying our result, we obtain a characterization of algebraic formal power series in terms of weighted logics. This generalizes a result of Lautemann, Schwentick and Thérien on context-free languages.

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Authors and Affiliations

  1. Institut für Informatik, Universität Leipzig, D-04009, Leipzig, Germany

    Christian Mathissen

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  1. Christian Mathissen
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Editor information

Luca Aceto Ivan Damgård Leslie Ann Goldberg Magnús M. Halldórsson Anna Ingólfsdóttir Igor Walukiewicz

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Mathissen, C. (2008). Weighted Logics for Nested Words and Algebraic Formal Power Series. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70583-3_19

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  • DOI: https://doi.org/10.1007/978-3-540-70583-3_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70582-6

  • Online ISBN: 978-3-540-70583-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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