  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.
