We present pumping lemmas for five classes of functions definable by fragments of weighted automata over the min-plus semiring, the max-plus semiring and the semiring of natural numbers. As a corollary we show that the hierarchy of functions definable by unambiguous, finitely-ambiguous, polynomially-ambiguous weighted automata, and the full class of weighted automata is strict for the min-plus and max-plus semirings.

@article{paperbot1297,
  title = {Pumping lemmas for weighted automata},
  author = {Agnishom Chattopadhyay and Filip Mazowiecki and Anca Muscholl and Cristian Riveros},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 17, Issue 3},
  year = {2021},
  doi = {10.46298/lmcs-17(3:7)2021}
}