Pumping lemmas for weighted automata

Abstract

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.

References in corpus (2)

• Deciding Unambiguity and Sequentiality starting from a Finitely Ambiguous Max-Plus Automaton
• Aperiodic Weighted Automata and Weighted First-Order Logic

Cited by in corpus (1)

• Aperiodic Weighted Automata and Weighted First-Order Logic