Berstel and Reutenauer ( 1988 ) give a sufficiently general finite-state framework to allow this : weights may fall in any set K ( instead of R ) .
rational series and their languages
Jean Berstel Christophe Reutenauer
We will enforce an invariant : the weight of any pathset H must be ( & EÎ  P ( Ï ) , & EÎ  P ( Ï ) val ( Ï ) ) E R > 0 x V , from which ( 1 ) is trivial to compute . Berstel and Reutenauer ( 1988 ) give a sufficiently general finite-state framework to allow this : weights may fall in any set K ( instead of R ) . Multiplication and addition are replaced by binary operations Â® and Â® on K. Thus Â® is used to combine arc weights into a path weight and Â® is used to combine the weights of alternative paths .
@@CITATION give a sufficiently general finite-state framework to allow this : weights may fall in any set K ( instead of R ) .