[PDF] Handbook Of Weighted Automata eBook

Author : Manfred Droste
Publisher : Springer Science & Business Media
Page : 614 pages
File Size : 18,1 MB
Release : 2009-09-18
Category : Computers
ISBN : 3642014925

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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.

Author : Manfred Droste
Publisher : Springer
Page : 608 pages
File Size : 14,92 MB
Release : 2009-09-28
Category : Computers
ISBN : 9783642014918

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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.

Author : Jacques Sakarovitch
Publisher : Cambridge University Press
Page : 818 pages
File Size : 48,71 MB
Release : 2009-10-01
Category : Mathematics
ISBN : 1139643797

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Automata theory lies at the foundation of computer science, and is vital to a theoretical understanding of how computers work and what constitutes formal methods. This treatise gives a rigorous account of the topic and illuminates its real meaning by looking at the subject in a variety of ways. The first part of the book is organised around notions of rationality and recognisability. The second part deals with relations between words realised by finite automata, which not only exemplifies the automata theory but also illustrates the variety of its methods and its fields of application. Many exercises are included, ranging from those that test the reader, to those that are technical results, to those that extend ideas presented in the text. Solutions or answers to many of these are included in the book.

Author : Laura Wirth
Publisher : Springer Nature
Page : 191 pages
File Size : 20,89 MB
Release : 2022-10-13
Category : Mathematics
ISBN : 3658393238

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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, 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.

Author : Sanjeev Arora
Publisher : Cambridge University Press
Page : 609 pages
File Size : 11,37 MB
Release : 2009-04-20
Category : Computers
ISBN : 0521424267

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New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Author : Grzegorz Rozenberg
Publisher : Springer Science & Business Media
Page : 654 pages
File Size : 17,90 MB
Release : 1997
Category : Computers
ISBN : 9783540606499

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This third volume of the Handbook of Formal Languages discusses language theory beyond linear or string models: trees, graphs, grids, pictures, computer graphics. Many chapters offer an authoritative self-contained exposition of an entire area. Special emphasis is on interconnections with logic.

Author : Paul C. Bell
Publisher : Springer Nature
Page : 181 pages
File Size : 50,46 MB
Release : 2021-10-25
Category : Computers
ISBN : 3030897168

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This book constitutes the refereed proceedings of the 15th International Conference on Reachability Problems, RP 2021, held in Liverpool, UK in October 2021. The 6 full papers presented were carefully reviewed and selected from 27 submissions. In addition, 4 invited papers were included in this volume. The RP proceedings cover topics such as reachability for infinite state systems; rewriting systems; reachability analysis in counter/timed/cellular/communicating automata; Petri nets; computational aspects of semigroups, groups, and rings; reachability in dynamical and hybrid systems; frontiers between decidable and undecidable reachability problems; complexity and decidability aspects; predictability in iterative maps; and new computational paradigms. Chapter ‘Recent Advances on Reachability Problems for Valence Systems’ is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Author : Giuseppe F Italiano
Publisher : Springer
Page : 482 pages
File Size : 30,45 MB
Release : 2015-08-10
Category : Computers
ISBN : 3662480573

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This two volume set LNCS 9234 and 9235 constitutes the refereed conference proceedings of the 40th International Symposium on Mathematical Foundations of Computer Science, MFCS 2015, held in Milan, Italy, in August 2015. The 82 revised full papers presented together with 5 invited talks were carefully selected from 201 submissions. The papers feature high-quality research in all branches of theoretical computer science. They have been organized in the following topical main sections: logic, semantics, automata, and theory of programming (volume 1) and algorithms, complexity, and games (volume 2).

Author : Werner Kuich
Publisher : Springer
Page : 372 pages
File Size : 28,28 MB
Release : 2011-11-06
Category : Computers
ISBN : 3642248977

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This Festschrift volume, published in honor of Symeon Bozapalidis on the occasion of his retirement after more than 35 years of teaching activity, focuses on the subjects taught by Symeon, namely: algebra, linear algebra, mathematical logic, number theory, automata theory, tree languages and series, algebraic semantics, and fuzzy languages. Since 1982 -- at the Aristotle University of Thessaloniki -- Symeon's main interests have been closely connected with the algebraic foundations in computer science. In particular, he contributed to the development of the theory of tree languages and series, the axiomatization of graphs, picture theory, and fuzzy languages. The volume contains 15 invited papers, written by colleagues, friends, and students of Symeon. All of the papers were carefully refereed and are connected to his research topics. Most of the papers were presented at the Workshop on Algebraic Foundations in Computer Science, held in Thessaloniki, Greece, during November 7--8, 2011.

Author : Mihai Codescu
Publisher : Springer
Page : 178 pages
File Size : 45,59 MB
Release : 2015-12-29
Category : Computers
ISBN : 3319281143

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This book constitutes the thoroughly refereed post-conference proceedings of the 22nd International Workshop on Algebraic Development Techniques, WADT 2014, held in September 2014 in Sinaia, Romania. The 8 revised papers presented were carefully reviewed and selected from 13 presentations and focus together with one invited paper on foundations of algebraic specification, approaches to formal specification including process calculi and models of concurrent, distributed and mobile computing, specification languages, methods, and environments, semantics of conceptual modeling methods and techniques, model-driven development, graph transformations, term rewriting and proof systems, integration of formal specification techniques, formal testing and quality assurance, validation, and verification.