2026-07-22T12:34:49Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14187 2024-03-06T10:53:42Z ddc:004 open_access

Optimal Spectral-Norm Approximate Minimization of Weighted Finite Automata Balle, Borja Lacroce, Clara Panangaden, Prakash Precup, Doina Rabusseau, Guillaume Weighted finite automata approximate minimization Hankel matrices AAK Theory 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Borja Balle and Clara Lacroce and Prakash Panangaden and Doina Precup and Guillaume Rabusseau 2021 Is Part Of LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2021.118 urn:nbn:de:0030-drops-141873 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.118 eng https://creativecommons.org/licenses/by/4.0/legalcode