Weighted Automata, Formal Power Series and Weighted Logic

2022 Mathematics

Author : Laura Wirth
Release : 2022
Genre : Mathematics
Kind : eBook
Book Rating : 329/5 ( reviews)

Book Synopsis Weighted Automata, Formal Power Series and Weighted Logic by : Laura Wirth

Download or read book Weighted Automata, Formal Power Series and Weighted Logic written by Laura Wirth. This book was released on 2022. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Weighted Automata, Formal Power Series and Weighted Logic

2022-10-13 Mathematics

Author : Laura Wirth
Release : 2022-10-13
Genre : Mathematics
Kind : eBook
Book Rating : 238/5 ( reviews)

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Book Synopsis Weighted Automata, Formal Power Series and Weighted Logic by : Laura Wirth

Download or read book Weighted Automata, Formal Power Series and Weighted Logic written by Laura Wirth. This book was released on 2022-10-13. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Weighted Automata

2009-09-18 Computers

Author : Manfred Droste
Release : 2009-09-18
Genre : Computers
Kind : eBook
Book Rating : 925/5 ( reviews)

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Book Synopsis Handbook of Weighted Automata by : Manfred Droste

Download or read book Handbook of Weighted Automata written by Manfred Droste. This book was released on 2009-09-18. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this Handbook is to highlight both theory and applications of weighted automata. Weighted finite automata are classical nondeterministic finite automata in which the transitions carry weights. These weights may model, e. g. , the cost involved when executing a transition, the amount of resources or time needed for this,or the probability or reliability of its successful execution. The behavior of weighted finite automata can then be considered as the function (suitably defined) associating with each word the weight of its execution. Clearly, weights can also be added to classical automata with infinite state sets like pushdown automata; this extension constitutes the general concept of weighted automata. To illustrate the diversity of weighted automata, let us consider the following scenarios. Assume that a quantitative system is modeled by a classical automaton in which the transitions carry as weights the amount of resources needed for their execution. Then the amount of resources needed for a path in this weighted automaton is obtained simply as the sum of the weights of its transitions. Given a word, we might be interested in the minimal amount of resources needed for its execution, i. e. , for the successful paths realizing the given word. In this example, we could also replace the “resources” by “profit” and then be interested in the maximal profit realized, correspondingly, by a given word.

Automata, Languages and Programming

2005-08-25 Computers

Author : Luis Caires
Release : 2005-08-25
Genre : Computers
Kind : eBook
Book Rating : 914/5 ( reviews)

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Book Synopsis Automata, Languages and Programming by : Luis Caires

Download or read book Automata, Languages and Programming written by Luis Caires. This book was released on 2005-08-25. Available in PDF, EPUB and Kindle. Book excerpt: The 32nd International Colloquium on Automata, Languages and Programming (ICALP 2005) was held in Lisbon, Portugal from July 11 to July 15, 2005. These proceedings contain all contributed papers presented at ICALP 2005, - getherwiththepapersbytheinvitedspeakersGiuseppeCastagna(ENS),Leonid Libkin (Toronto), John C. Mitchell (Stanford), Burkhard Monien (Paderborn), and Leslie Valiant (Harvard). The program had an additional invited lecture by Adi Shamir (Weizmann Institute) which does not appear in these proceedings. ICALP is a series of annual conferences of the European Association for Theoretical Computer Science (EATCS). The ?rst ICALP took place in 1972. This year, the ICALP program consisted of the established track A (focusing on algorithms, automata, complexity and games) and track B (focusing on logic, semantics and theory of programming), and innovated on the structure of its traditional scienti?c program with the inauguration of a new track C (focusing on security and cryptography foundation). In response to a call for papers, the Program Committee received 407 s- missions, 258 for track A, 75 for track B and 74 for track C. This is the highest number of submitted papers in the history of the ICALP conferences. The P- gram Committees selected 113 papers for inclusion in the scienti?c program. In particular, the Program Committee for track A selected 65 papers, the P- gram Committee for track B selected 24 papers, and the Program Committee for track C selected 24 papers. All the work of the Program Committees was done electronically.

Developments in Language Theory

2006-06-22 Mathematics

Author : Oscar H. Ibarra
Release : 2006-06-22
Genre : Mathematics
Kind : eBook
Book Rating : 301/5 ( reviews)

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Book Synopsis Developments in Language Theory by : Oscar H. Ibarra

Download or read book Developments in Language Theory written by Oscar H. Ibarra. This book was released on 2006-06-22. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Conference on Developments in Language Theory, DLT 2006, held in Santa Barbara, CA, June 2006. The book presents 36 revised full papers together with 4 invited papers. All important issues in language theory are addressed including grammars, acceptors and transducers for strings, trees, graphs, arrays; efficient text algorithms; algebraic theories for automata and languages; and more.

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