Derivatives of rational expressions and related theorems

Authors:
Jean-Marc Champarnaud;Gérard Duchamp
Affiliations:
LIFAR, Faculté des Sciences et des Techniques, University of Rouen, Place E Blondel, 76821 Mont-Saint-Aignan, Cedex, France;LIFAR, Faculté des Sciences et des Techniques, University of Rouen, Place E Blondel, 76821 Mont-Saint-Aignan, Cedex, France
Venue:
Theoretical Computer Science - Implementation and application automata
Year:
2004

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Abstract

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, multiplicity analogues of the well known theorems of Brzozowski and Antimirov are provided.