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Weighted Tree Automata over Valuation Monoids and Their Characterization by Weighted Logics

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Algebraic Foundations in Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7020))

Abstract

Quantitative aspects of systems can be modeled by weighted automata. Here, we deal with such automata running on finite trees. Usually, transitions are weighted with elements of a semiring and the behavior of the automaton is obtained by multiplying the weights along a run. We turn to a more general cost model: the weight of a run is now determined by a global valuation function. An example of such a valuation function is the average of the weights. We establish a characterization of the behaviors of these weighted finite tree automata by fragments of weighted monadic second-order logic. For bi-locally finite bimonoids, we show that weighted tree automata capture the expressive power of several semantics of full weighted MSO logic. Decision procedures follow as consequences.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Leipzig, D-04109, Leipzig, Germany

    Manfred Droste, Doreen Götze & Ingmar Meinecke

  2. Institut für Angewandte Informatik e.V., Universität Leipzig, D-04109, Leipzig, Germany

    Steffen Märcker

Authors
  1. Manfred Droste
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  2. Doreen Götze
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  3. Steffen Märcker
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  4. Ingmar Meinecke
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Editors and Affiliations

  1. Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Austria

    Werner Kuich

  2. Department of Mathematics, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    George Rahonis

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Droste, M., Götze, D., Märcker, S., Meinecke, I. (2011). Weighted Tree Automata over Valuation Monoids and Their Characterization by Weighted Logics. In: Kuich, W., Rahonis, G. (eds) Algebraic Foundations in Computer Science. Lecture Notes in Computer Science, vol 7020. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24897-9_2

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  • DOI: https://doi.org/10.1007/978-3-642-24897-9_2

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  • Print ISBN: 978-3-642-24896-2

  • Online ISBN: 978-3-642-24897-9

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