From Hadamard Expressions to Weighted Rotating Automata and Back
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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.
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