Regularly controlled formal power series

Regulated rewriting is one of the classical topics in formal language theory, see [3, 2]. This paper starts the research of regulated rewriting in the framework of formal power series, cf. [6, 7, 9]. More specifically, we model what is known as “free derivations” and “leftmost derivations of type 1” within context-free grammars controlled by regular sets in the language case. We show that the class which is the formal power series analogue of controlled free derivations forms a semiring containing the semiring of algebraic series, which in turn is characterized by the formal power series analogue of controlled leftmost derivations of type 1.

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