The support of a recognizable series over a zero-sum free, commutative semiring is recognizable

Abstract

We show that the support of a recognizable series over a zero-sum free, commutative semiring is a recognizable language. We also give a sufficient and necessary condition for the existence of an effective transformation of a weighted automaton recognizing a series S over a zero-sum free, commutative semiring into an automaton recognizing the support of S.