Titlebook: Weighted Automata, Formal Power Series and Weighted Logic; Laura Wirth Book 2022 The Editor(s) (if applicable) and The Author(s), under ex

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Languages, Automata and Monadic Second-Order Logic,he starting point of those in the weighted setting that will be considered in the subsequent chapters. Throughout this chapter, we further establish a clear overview over the classical results from Theoretical Computer Science, whose extensions and generalizations we will derive in the subsequent chapters.

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,The Kleene–Schützenberger Theorem,ve extensions of the classical ones. In doing so, he extended the language-theoretic concept of recognizability to formal power series with coefficients in an arbitrary semiring. On the other hand, Schützenberger also investigated rational power series, which form a generalization of rational languages.

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Weighted Monadic Second-Order Logic and Weighted Automata,eighted automata, and characterized their behaviors as rational formal power series. Hence, he established a generalization of Kleene’s Theorem, which we have presented in Chapter 4. In 2005, Droste and Gastin [5] extended the Büchi–Elgot–Trakhtenbrot Theorem to the realm of formal power series.

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978-3-658-39322-9The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Fachmedien Wies

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