Arden's rule and the Kleene-Schützenberger theorem

We will take a look at a classical result by Schützenberger, generalizing Kleene's theorem to formal power series, and give a proof of this result that closely resembles Rutten's coinductive proof of Kleene's theorem (1998). It turns out that the key ingredient of a proof consists of a combination of induction with application of Arden's rule, guaranteeing the existence of unique solutions to certain types of systems of equations.  

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