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A Nivat Theorem for Weighted Picture Automata and Weighted MSO Logic

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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))

Abstract

Picture languages have been intensively investigated by several research groups. In this paper, we define weighted two-dimensional on-line tessellation automata (W2OTA) taking weights from a new weight structure called picture valuation monoid. The behavior of this automaton model is a picture series mapping pictures over an alphabet to a picture valuation monoid. As one of our main results, we prove a Nivat theorem for W2OTA. It shows that recognizable picture series can be obtained precisely as projections of particularly simple unambiguously recognizable series restricted to unambiguous recognizable picture languages. In addition, we introduce a weighted MSO logic which can model average density of pictures. As the other main result of this paper, we show that W2OTA and a suitable fragment of our weighted MSO logics are expressively equivalent.

P. Babari: Supported by DFG Graduiertenkolleg 1763 (QuantLA).

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Authors and Affiliations

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

    Parvaneh Babari & Manfred Droste

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  1. Parvaneh Babari
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  2. Manfred Droste
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Correspondence to Parvaneh Babari .

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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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Babari, P., Droste, M. (2015). A Nivat Theorem for Weighted Picture Automata and Weighted MSO Logic. 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_55

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  • DOI: https://doi.org/10.1007/978-3-319-15579-1_55

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-15579-1

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