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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2019.76
URN: urn:nbn:de:0030-drops-110203
URL: http://drops.dagstuhl.de/opus/volltexte/2019/11020/
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Droste, Manfred ; Gastin, Paul

Aperiodic Weighted Automata and Weighted First-Order Logic

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LIPIcs-MFCS-2019-76.pdf (0.5 MB)


Abstract

By fundamental results of Schützenberger, McNaughton and Papert from the 1970s, the classes of first-order definable and aperiodic languages coincide. Here, we extend this equivalence to a quantitative setting. For this, weighted automata form a general and widely studied model. We define a suitable notion of a weighted first-order logic. Then we show that this weighted first-order logic and aperiodic polynomially ambiguous weighted automata have the same expressive power. Moreover, we obtain such equivalence results for suitable weighted sublogics and finitely ambiguous or unambiguous aperiodic weighted automata. Our results hold for general weight structures, including all semirings, average computations of costs, bounded lattices, and others.

BibTeX - Entry

@InProceedings{droste_et_al:LIPIcs:2019:11020,
  author =	{Manfred Droste and Paul Gastin},
  title =	{{Aperiodic Weighted Automata and Weighted First-Order Logic}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{76:1--76:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Peter Rossmanith and Pinar Heggernes and Joost-Pieter Katoen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11020},
  URN =		{urn:nbn:de:0030-drops-110203},
  doi =		{10.4230/LIPIcs.MFCS.2019.76},
  annote =	{Keywords: Weighted automata, weighted logic, aperiodic automata, first-order logic, unambiguous, finitely ambiguous, polynomially ambiguous}
}

Keywords: Weighted automata, weighted logic, aperiodic automata, first-order logic, unambiguous, finitely ambiguous, polynomially ambiguous
Seminar: 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)
Issue Date: 2019
Date of publication: 23.08.2019


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