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Weighted Automata and Weighted Logics with Discounting

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Implementation and Application of Automata (CIAA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4783))

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Abstract

We introduce a weighted logic with discounting and we establish Büchi’s and Elgot’s theorem for weighted automata over finite words and arbitrary commutative semirings. Then we investigate Büchi and Muller automata with discounting over the max-plus and the min-plus semiring. We show their expressive equivalence with weighted MSO-sentences with discounting. In this case our logic has a purely syntactic definition. For the finite case, we obtain a purely syntactically defined weighted logic if the underlying semiring is additively locally finite.

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Author information

Authors and Affiliations

  1. Institute of Computer Science, Leipzig University, D-04009 Leipzig, Germany

    Manfred Droste

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

    George Rahonis

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  1. Manfred Droste
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  2. George Rahonis
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Jan Holub Jan Žďárek

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Droste, M., Rahonis, G. (2007). Weighted Automata and Weighted Logics with Discounting. In: Holub, J., Žďárek, J. (eds) Implementation and Application of Automata. CIAA 2007. Lecture Notes in Computer Science, vol 4783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76336-9_9

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  • DOI: https://doi.org/10.1007/978-3-540-76336-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76335-2

  • Online ISBN: 978-3-540-76336-9

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