國立虎尾科技大學 |

Weighted Automata, Formal Power Series and Weighted Logic

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Weighted Automata, Formal Power Series and Weighted Logic/ by Laura Wirth.
作者:	Wirth, Laura.
面頁冊數:	XI, 190 p. 63 illus. Textbook for German language market.online resource. :
Contained By:	Springer Nature eBook
標題:	Computational Science and Engineering. -
電子資源:	https://doi.org/10.1007/978-3-658-39323-6
ISBN:	9783658393236

Weighted Automata, Formal Power Series and Weighted Logic
Wirth, Laura.

Weighted Automata, Formal Power Series and Weighted Logic[electronic resource] /by Laura Wirth. - 1st ed. 2022. - XI, 190 p. 63 illus. Textbook for German language market.online resource. - BestMasters,2625-3615. - BestMasters,.

Introduction -- Languages, Automata and Monadic Second-Order Logic -- Weighted Automata -- The Kleene–Schützenberger Theorem -- Weighted Monadic Second-Order Logic and Weighted Automata -- Summary and Further Research.

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. The Author 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.

ISBN: 9783658393236

Standard No.: 10.1007/978-3-658-39323-6doiSubjects--Topical Terms:

670319
Computational Science and Engineering.

LC Class. No.: QA71-90

Dewey Class. No.: 518

Weighted Automata, Formal Power Series and Weighted Logic
LDR:03078nam a22003735i 4500 001 1084267
003 DE-He213
005 20221013064300.0
007 cr nn 008mamaa
008 221228s2022 gw | s |||| 0|eng d
020 $a 9783658393236 $9 978-3-658-39323-6
024 7 $a 10.1007/978-3-658-39323-6 $2 doi
035 $a 978-3-658-39323-6
050 4 $a QA71-90
072 7 $a PBKS $2 bicssc
072 7 $a MAT006000 $2 bisacsh
072 7 $a PBKS $2 thema
082 0 4 $a 518 $2 23
100 1 $a Wirth, Laura. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1390513
245 1 0 $a Weighted Automata, Formal Power Series and Weighted Logic $h [electronic resource] / $c by Laura Wirth.
250 $a 1st ed. 2022.
264 1 $a Wiesbaden : $b Springer Fachmedien Wiesbaden : $b Imprint: Springer Spektrum, $c 2022.
300 $a XI, 190 p. 63 illus. Textbook for German language market. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a BestMasters, $x 2625-3615
505 0 $a Introduction -- Languages, Automata and Monadic Second-Order Logic -- Weighted Automata -- The Kleene–Schützenberger Theorem -- Weighted Monadic Second-Order Logic and Weighted Automata -- Summary and Further Research.
520 $a 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. The Author 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.
650 2 4 $a Computational Science and Engineering. $3 670319
650 1 4 $a Computational Mathematics and Numerical Analysis. $3 669338
650 0 $a Mathematics—Data processing. $3 1365953
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783658393229
776 0 8 $i Printed edition: $z 9783658393243
830 0 $a BestMasters, $x 2625-3577 $3 1253531
856 4 0 $u https://doi.org/10.1007/978-3-658-39323-6
912 $a ZDB-2-SNA
950 $a Life Science and Basic Disciplines (German Language) (SpringerNature-11777)