Handbook of Weighted Automata

1. Front Matter

   Pages I-XVII

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2. Foundations

   1. Front Matter

      Pages 1-1

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   2. Semirings and Formal Power Series

      • Manfred Droste, Werner Kuich

      Pages 3-28

   3. Fixed Point Theory

      • Zoltán Ésik

      Pages 29-65

3. Concepts of Weighted Recognizability

   1. Front Matter

      Pages 67-67

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   2. Finite Automata

      • Zoltán Ésik, Werner Kuich

      Pages 69-104

   3. Rational and Recognisable Power Series

      • Jacques Sakarovitch

      Pages 105-174

   4. Weighted Automata and Weighted Logics

      • Manfred Droste, Paul Gastin

      Pages 175-211

   5. Weighted Automata Algorithms

      • Mehryar Mohri

      Pages 213-254

4. Weighted Discrete Structures

   1. Front Matter

      Pages 255-255

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   2. Algebraic Systems and Pushdown Automata

      • Ion Petre, Arto Salomaa

      Pages 257-289

   3. Lindenmayer Systems

      • Juha Honkala

      Pages 291-311

   4. Weighted Tree Automata and Tree Transducers

      • Zoltán Fülöp, Heiko Vogler

      Pages 313-403

   5. Traces, Series-Parallel Posets, and Pictures: A Weighted Study

      • Ina Fichtner, Dietrich Kuske, Ingmar Meinecke

      Pages 405-450

5. Applications

   1. Front Matter

      Pages 451-451

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   2. Digital Image Compression

      • Jürgen Albert, Jarkko Kari

      Pages 453-479

   3. Fuzzy Languages

      • George Rahonis

      Pages 481-517

   4. Model Checking Linear-Time Properties of Probabilistic Systems

      • Christel Baier, Marcus Größer, Frank Ciesinski

      Pages 519-570

   5. Applications of Weighted Automata in Natural Language Processing

      • Kevin Knight, Jonathan May

      Pages 571-596

6. Back Matter

   Pages 597-608

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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.

• Automat
• Extension
• algorithms
• automata
• cognition
• finite automata
• formal language
• logic
• model checking
• natural language
• speech recognition
• theoretical computer science

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)

• Inst. Informatik, Universität Leipzig, Leipzig, Germany

  Manfred Droste

• Institut für Diskrete, TU Wien, Wien, Austria

  Werner Kuich

• Fak. Informatik, TU Dresden, Dresden, Germany

  Heiko Vogler

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