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Kleene and Büchi Theorems for Weighted Automata and Multi-valued Logics over Arbitrary Bounded Lattices

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Developments in Language Theory (DLT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6224))

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Abstract

We show that \({\mathcal L}\)-weighted automata, \({\mathcal L}\)-rational series, and \(\mathcal L\)-valued monadic second-order logic have the same expressive power, for any bounded lattice \(\mathcal L\) and for finite and infinite words. This extends classical results of Kleene and Büchi to arbitrary bounded lattices, without any distributivity assumption that is fundamental in the theory of weighted automata over semirings. In fact, we obtain these results for large classes of strong bimonoids which properly contain all bounded lattices.

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Author information

Authors and Affiliations

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

    Manfred Droste

  2. Department of Computer Science, TU Dresden, 01062, Dresden, Germany

    Heiko Vogler

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  1. Manfred Droste
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  2. Heiko Vogler
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Editors and Affiliations

  1. Dept. of Computer Science, University of Western Ontario, N6A 5B7, London, ON, Canada

    Yuan Gao , Hanlin Lu , Shinnosuke Seki  & Sheng Yu , ,  & 

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Droste, M., Vogler, H. (2010). Kleene and Büchi Theorems for Weighted Automata and Multi-valued Logics over Arbitrary Bounded Lattices. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds) Developments in Language Theory. DLT 2010. Lecture Notes in Computer Science, vol 6224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14455-4_16

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  • DOI: https://doi.org/10.1007/978-3-642-14455-4_16

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