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, B�chi, Elgot and Trakhtenbrot, which concentrate on the expressive power of finite automata. We further derive a generalization of the B�chi-Elgot-Trakhtenbrot Theorem addressing formulas, whereas the original statement ...
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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, B�chi, Elgot and Trakhtenbrot, which concentrate on the expressive power of finite automata. We further derive a generalization of the B�chi-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 Sch�tzenberger's extension of Kleene's Theorem, referred to as Kleene-Sch�tzenberger 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 B�chi-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.
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Add this copy of Weighted Automata, Formal Power Series and Weighted to cart. $51.65, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Springer Spektrum.
Add this copy of Weighted Automata, Formal Power Series and Weighted to cart. $71.22, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2022 by Springer Spektrum.
