Weighted Automata, Formal Power Series and Weighted Logic - Couverture souple

Wirth, Laura

Couverture souple

ISBN 10 : 365839322X ISBN 13 : 9783658393229

Editeur : Springer Spektrum, 2022

Synopsis

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, Büchi, Elgot and Trakhtenbrot, which concentrate on the expressive power of finite automata. We further derive a generalization of the Büchi-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 Schützenberger's extension of Kleene's Theorem, referred to as Kleene-Schützenberger 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 Büchi-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.

A propos du livre

À propos de l'auteur

Laura Wirth completed her Master's thesis in Mathematics at the University of Konstanz in 2022. It was supervised by Prof. Salma Kuhlmann as well as Prof. Sven Kosub and received the highest grade with honors.

Détails de l'édition

• Éditeur: Springer Spektrum
• Date d'édition: 2022
• Langue: anglais
• ISBN 10: 365839322X
• ISBN 13: 9783658393229
• Reliure: Broché
• Numéro d'édition: 1
• Nombre de pages: 204
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne