Weighted Automata, Formal Power Series and Weighted Logic

Name: Weighted Automata, Formal Power Series and Weighted Logic
Brand: Springer Nature
SKU: 9783658393236
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Springer Nature

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9783658393236

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The main objective of this work is to represent the behaviors of weighted automata by expressively equivalent formalisms: rational operations on formal power series, linear representations by means of matrices, and weighted monadic second-order logic. First, we exhibit the classical results of Kleene, Bchi, Elgot and Trakhtenbrot, which concentrate on the expressive power of finite automata. We further derive a generalization of the BchiElgotTrakhtenbrot Theorem addressing formulas, whereas the original statement concerns only sentences. Then we use the language-theoretic methods as starting point for our investigations regarding power series. We establish Schtzenbergers extension of Kleenes Theorem, referred to as KleeneSchtzenberger Theorem. Moreover, we introduce a weighted version of monadic second-order logic, which is due to Droste and Gastin. By means of this weighted logic, we derive an extension of the BchiElgotTrakhtenbrot Theorem. Thus, we point out relations among the different specification approaches for formal power series. Further, we relate the notions and results concerning power series to their counterparts in Language Theory. Overall, our investigations shed light on the interplay between languages, formal power series, automata and monadic second-order logic.

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