Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Bohn, León; Löding, Christof https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-164553
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Passive Learning of Deterministic Büchi Automata by Combinations of DFAs

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Abstract

We present an algorithm that constructs a deterministic Büchi automaton in polynomial time from given sets of positive and negative example words. This learner constructs multiple DFAs using a polynomial-time active learning algorithm on finite words as black box using an oracle that we implement based on the given sample of ω-words, and combines these DFAs into a single DBA. We prove that the resulting algorithm can learn a DBA for each DBA-recognizable language in the limit by providing a characteristic sample for each DBA-recognizable language. We can only guarantee completeness of our algorithm for the full class of DBAs through characteristic samples that are, in general, exponential in the size of a minimal DBA for the target language. But we show that for each fixed k these characteristic samples are of polynomial size for the class of DBAs in which each subset of pairwise language-equivalent states has size at most k.

BibTeX - Entry

@InProceedings{bohn_et_al:LIPIcs.ICALP.2022.114,
  author =	{Bohn, Le\'{o}n and L\"{o}ding, Christof},
  title =	{{Passive Learning of Deterministic B\"{u}chi Automata by Combinations of DFAs}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{114:1--114:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16455},
  URN =		{urn:nbn:de:0030-drops-164553},
  doi =		{10.4230/LIPIcs.ICALP.2022.114},
  annote =	{Keywords: deterministic B\"{u}chi automata, learning from examples, learning in the limit, active learning}
}

Keywords: deterministic Büchi automata, learning from examples, learning in the limit, active learning
Seminar: 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)
Issue date: 2022
Date of publication: 28.06.2022


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