2001 | OriginalPaper | Buchkapitel
Rational Transformations of Formal Power Series
verfasst von : Manfred Droste, Guo-Qiang Zhang
Erschienen in: Automata, Languages and Programming
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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Formal power series are an extension of formal languages. Recognizable formal power series can be captured by the so-called weighted finite automata, generalizing finite state machines. In this paper, motivated by codings of formal languages, we introduce and investigate two types of transformations for formal power series. We characterize when these transformations preserve rationality, generalizing the recent results of Zhang [15] to the formal power series setting. We show, for example, that the “square-root” operation, while preserving regularity for formal languages, preserves rationality for formal power series when the underlying semiring is commutative or locally finite, but not in general.