Weighted automata with storage

Abstract

We consider finite-state automata that are equipped with a storage. Moreover, the transitions are weighted by elements of a unital valuation monoid. A weighted automaton with storage recognizes a weighted language, which is a mapping from input strings to elements of the carrier set of the unital valuation monoid. For the class of weighted languages recognizable by such automata we prove closure properties, a Chomsky-Schützenberger theorem, and a Büchi-Elgot-Trakhtenbrot theorem. In case of idempotent, locally finite, and sequential unital valuation monoids, the recognized weighted languages are step functions.