Brzozowski's Derivatives Extended to Multiplicities

Our aim is to study the set of K-rational expressions describing rational series. More precisely we are concerned with the definition of quotients of this set by coarser and coarser congruences which lead to an extension - in the case of multiplicities - of some classical results stated in the Boolean case. In particular, analogues of the well known theorems of Brzozowski and Antimirov are provided in this frame.

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