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Weighted Automata, Formal Power Series and Weighted Logic

Weighted Automata, Formal Power Series and Weighted Logic

by Laura Wirth
Paperback
Publication Date: 14/10/2022

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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, Buchi, Elgot and Trakhtenbrot, which concentrate on the expressive power of finite automata. We further derive a generalization of the Buchi-Elgot-Trakhtenbrot 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 Schutzenberger's extension of Kleene's Theorem, referred to as Kleene-Schutzenberger 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 Buchi-Elgot-Trakhtenbrot 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.
ISBN:
9783658393229
9783658393229
Category:
Numerical analysis
Format:
Paperback
Publication Date:
14-10-2022
Publisher:
Springer Fachmedien Wiesbaden
Country of origin:
Germany
Pages:
190
Dimensions (mm):
210x148mm
Weight:
0.27kg

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