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International Conference on Developments in Language Theory

DLT 2016: Developments in Language Theory pp 151–163Cite as

Weighted Automata and Logics on Infinite Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9840))

Abstract

We show a Büchi-like connection between graph automata and logics for infinite graphs. Using valuation monoids, a very general weight structure able to model computations like average or discounting, we extend this result to the quantitative setting. This gives us the first general results connecting automata and logics over infinite graphs in the qualitative and the quantitative setting.

S. Dück—Supported by Deutsche Forschungsgemeinschaft (DFG) Graduiertenkolleg 1763 (QuantLA).

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Notes

  1. 1.

    [14] enforced \({{\mathrm{Val}}}(d)=d\), which was later shown to be not required even in the word case, see e.g. [21].

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Acknowledgments

I want to thank Manfred Droste and Tobias Weihrauch for helpful discussions and insightful remarks on earlier drafts of this paper.

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Authors and Affiliations

  1. Institute of Computer Science, Leipzig University, 04109, Leipzig, Germany

    Stefan Dück

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  1. Stefan Dück
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Correspondence to Stefan Dück .

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Editors and Affiliations

  1. Université du Québec à Montréal , Montreal, Québec, Canada

    Srečko Brlek

  2. Dept Mathematiques, Univ du Quebec Montreal Dept Mathematiques, Montreal, Québec, Canada

    Christophe Reutenauer

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Dück, S. (2016). Weighted Automata and Logics on Infinite Graphs. In: Brlek, S., Reutenauer, C. (eds) Developments in Language Theory. DLT 2016. Lecture Notes in Computer Science(), vol 9840. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53132-7_13

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  • DOI: https://doi.org/10.1007/978-3-662-53132-7_13

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