What's Decidable about Weighted Automata?

@inproceedings{Almagor2011WhatsDA,
  title={What's Decidable about Weighted Automata?},
  author={Shaull Almagor and Udi Boker and Orna Kupferman},
  booktitle={ATVA},
  year={2011}
}
Weighted automata map input words to numerical values. Applications of weighted automata include formal verification of quantitative properties, as well as text, speech, and image processing. In the 90's, Krob studied the decidability of problems on rational series, which strongly relate to weighted automata. In particular, it follows from Krob's results that the universality problem (that is, deciding whether the values of all words are below some threshold) is decidable for weighted… 
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