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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Introduction, on the application context, a suitable representation or specification is chosen in order to interpret the information in a targeted manner. More precisely, the processing of data, and in particular the amount of resources required for this, depends on the chosen method or formal model for the repr

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Languages, Automata and Monadic Second-Order Logic,dering the classical notions and results in the context of languages, finite automata and monadic second-order logic. These classical formalisms are the starting point of those in the weighted setting that will be considered in the subsequent chapters. Throughout this chapter, we further establish a

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Languages, Automata and Monadic Second-Order Logic,dering the classical notions and results in the context of languages, finite automata and monadic second-order logic. These classical formalisms are the starting point of those in the weighted setting that will be considered in the subsequent chapters. Throughout this chapter, we further establish a

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Weighted Monadic Second-Order Logic and Weighted Automata,cond-order logic. At the same time, Schützenberger [37] investigated formal power series in the context of Automata Theory, introduced the notion of weighted automata, and characterized their behaviors as rational formal power series. Hence, he established a generalization of Kleene’s Theorem, which

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Book 2022l power series, linear representations by means of matrices, and weighted monadic second-order logic. .First, we exhibit the classical results of Kleene, Büchi, Elgot and Trakhtenbrot, which concentrate on the expressive power of finite automata. We further derive a generalization of the Büchi–Elgot