License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2019.17
URN: urn:nbn:de:0030-drops-109198
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10919/
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Michaliszyn, Jakub ; Otop, Jan

Approximate Learning of Limit-Average Automata

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LIPIcs-CONCUR-2019-17.pdf (0.5 MB)

Abstract

Limit-average automata are weighted automata on infinite words that use average to aggregate the weights seen in infinite runs. We study approximate learning problems for limit-average automata in two settings: passive and active. In the passive learning case, we show that limit-average automata are not PAC-learnable as samples must be of exponential-size to provide (with good probability) enough details to learn an automaton. We also show that the problem of finding an automaton that fits a given sample is NP-complete. In the active learning case, we show that limit-average automata can be learned almost-exactly, i.e., we can learn in polynomial time an automaton that is consistent with the target automaton on almost all words. On the other hand, we show that the problem of learning an automaton that approximates the target automaton (with perhaps fewer states) is NP-complete. The abovementioned results are shown for the uniform distribution on words. We briefly discuss learning over different distributions.

BibTeX - Entry

@InProceedings{michaliszyn_et_al:LIPIcs:2019:10919,
  author =	{Jakub Michaliszyn and Jan Otop},
  title =	{{Approximate Learning of Limit-Average Automata}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Wan Fokkink and Rob van Glabbeek},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10919},
  URN =		{urn:nbn:de:0030-drops-109198},
  doi =		{10.4230/LIPIcs.CONCUR.2019.17},
  annote =	{Keywords: weighted automata, learning, expected value}
}

Keywords: weighted automata, learning, expected value
Collection: 30th International Conference on Concurrency Theory (CONCUR 2019)
Issue Date: 2019
Date of publication: 20.08.2019

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