Alternating weighted automata over commutative semirings

We define and study alternating weighted automata over an arbitrary commutative semiring. Our model generalises the concept of alternation of existential and universal states in the classical Boolean setting to alternation of states performing addition and multiplication in the underlying commutative semiring. We completely characterise the class of commutative semirings S, for which alternating and non-alternating weighted automata over S are equally powerful, and we study some closure properties of the classes of formal power series realised by alternating weighted automata.