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Weighted Automata and Logics on Graphs

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Book cover Mathematical Foundations of Computer Science 2015 (MFCS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9234))

Abstract

Weighted automata model quantitative features of the behavior of systems and have been investigated for various structures like words, trees, traces, pictures, and nested words. In this paper, we introduce a general model of weighted automata acting on graphs, which form a quantitative version of Thomas’ unweighted model of graph acceptors. We derive a Nivat theorem for weighted graph automata which shows that their behaviors are precisely those obtainable from very particular weighted graph automata and unweighted graph acceptors with a few simple operations. We also show that a suitable weighted MSO logic is expressively equivalent to weighted graph automata. As a consequence, we obtain corresponding Büchi-type equivalence results known from the recent literature for weighted automata and weighted logics on words, trees, pictures, and nested words. Establishing such a general result has been an open problem for weighted logic for some time.

S. Dück—supported by Deutsche Forschungsgemeinschaft (DFG), project DR 202/11-1 and Graduiertenkolleg 1763 (QuantLA).

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Authors and Affiliations

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

    Manfred Droste & Stefan Dück

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  1. Manfred Droste
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  2. Stefan Dück
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Correspondence to Stefan Dück .

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Editors and Affiliations

  1. Università di Roma "Tor Vergata", Rome, Italy

    Giuseppe F Italiano

  2. Università degli Studi di Milano, Milan, Italy

    Giovanni Pighizzini

  3. University of Edinburgh, Edinburgh, United Kingdom

    Donald T. Sannella

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Droste, M., Dück, S. (2015). Weighted Automata and Logics on Graphs. In: Italiano, G., Pighizzini, G., Sannella, D. (eds) Mathematical Foundations of Computer Science 2015. MFCS 2015. Lecture Notes in Computer Science(), vol 9234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48057-1_15

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  • DOI: https://doi.org/10.1007/978-3-662-48057-1_15

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