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DOI: 10.4230/LIPIcs.ICALP.2021.118

Optimal Spectral-Norm Approximate Minimization of Weighted Finite Automata

Authors: Borja Balle, Clara Lacroce, Prakash Panangaden, Doina Precup, and Guillaume Rabusseau

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract

We address the approximate minimization problem for weighted finite automata (WFAs) with weights in ℝ, over a one-letter alphabet: to compute the best possible approximation of a WFA given a bound on the number of states. This work is grounded in Adamyan-Arov-Krein approximation theory, a remarkable collection of results on the approximation of Hankel operators. In addition to its intrinsic mathematical relevance, this theory has proven to be very effective for model reduction. We adapt these results to the framework of weighted automata over a one-letter alphabet. We provide theoretical guarantees and bounds on the quality of the approximation in the spectral and 𝓁² norm. We develop an algorithm that, based on the properties of Hankel operators, returns the optimal approximation in the spectral norm.

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Borja Balle, Clara Lacroce, Prakash Panangaden, Doina Precup, and Guillaume Rabusseau. Optimal Spectral-Norm Approximate Minimization of Weighted Finite Automata. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 118:1-118:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{balle_et_al:LIPIcs.ICALP.2021.118,
  author =	{Balle, Borja and Lacroce, Clara and Panangaden, Prakash and Precup, Doina and Rabusseau, Guillaume},
  title =	{{Optimal Spectral-Norm Approximate Minimization of Weighted Finite Automata}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{118:1--118:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.118},
  URN =		{urn:nbn:de:0030-drops-141873},
  doi =		{10.4230/LIPIcs.ICALP.2021.118},
  annote =	{Keywords: Weighted finite automata, approximate minimization, Hankel matrices, AAK Theory}
}

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Optimal Spectral-Norm Approximate Minimization of Weighted Finite Automata

Abstract

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