## Derivation of rational expressions with multiplicity.(English)Zbl 1014.68085

Diks, Krzysztof (ed.) et al., Mathematical foundations of computer science 2002. 27th symposium, MFCS 2002, Warsaw, Poland, August 26-30, 2002. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 2420, 471-482 (2002).
Summary: This paper introduces a generalization of the partial derivatives of rational expressions, due to Antimirov, to rational expressions with multiplicity. We define the derivation of a rational expression with multiplicity in such a way that the result is a polynomial of expressions. This amounts to interpreting the addition symbol at the upper level in the semiring of coefficients.
Former results of Brzozowski and of Antimirov are then expressed in that framework that allows to deal with rational power series, and automata and expressions with multiplicity as well.
For the entire collection see [Zbl 0997.00033].

### MSC:

 68Q45 Formal languages and automata
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