Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Monographs in Theoretical Computer Science. An EATCS Series (EATCS)
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About this book
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.
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Table of contents (14 chapters)
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Front Matter
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Foundations
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Front Matter
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Concepts of Weighted Recognizability
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Front Matter
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Weighted Discrete Structures
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Front Matter
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Back Matter
Reviews
From the reviews:
"This book is an excellent reference for researchers in the field, as well as students interested in this research area. The presentation of applications makes it interesting to researchers from other fields to study weighted automata. ... One of the main arguments in favor of this handbook is the completeness of its index table — usually a faulty section in such volumes. The chapters are globally well-written and self-contained, thus pleasant to read, and the efforts put to maintain consistency in vocabulary thorough the book are very appreciable." (Michaël Cadilhac, The Book Review Column 43-3, 2012)
“The book presents a broad survey, theory and applications, of weighted automata, classical nondeterministic automata in which transitions carry weights. … The individual articles are written by well-known researchers in the field: they include extensive lists of references and many open problems. The book is valuable for both computer scientists and mathematicians (being interested in discrete structures).” (Cristian S. Calude, Zentralblatt MATH, Vol. 1200, 2011)
Editors and Affiliations
Bibliographic Information
Book Title: Handbook of Weighted Automata
Editors: Manfred Droste, Werner Kuich, Heiko Vogler
Series Title: Monographs in Theoretical Computer Science. An EATCS Series
DOI: https://doi.org/10.1007/978-3-642-01492-5
Publisher: Springer Berlin, Heidelberg
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2009
Hardcover ISBN: 978-3-642-01491-8Published: 28 September 2009
Softcover ISBN: 978-3-642-26049-0Published: 14 March 2012
eBook ISBN: 978-3-642-01492-5Published: 18 September 2009
Series ISSN: 1431-2654
Series E-ISSN: 2193-2069
Edition Number: 1
Number of Pages: XVII, 608
Topics: Theory of Computation, Logics and Meanings of Programs, Natural Language Processing (NLP), Mathematical Logic and Formal Languages, Computation by Abstract Devices, Mathematical Logic and Foundations