From hadamard expressions to weighted rotating automata and back

Abstract

This paper deals with the conversion of expressions denoting Hadamard series into weighted rotating automata. We prove that any algorithm converting rational series into one-way weighted automata can be extended to provide an algorithm which achieves our goal. We apply this to define the derivation and the follow automata of a Hadamard expression. Our method is also used to extend algorithms which perform the inverse conversion, up to some adjustment in order to fulfill some constraints.