© 2009

Handbook of Weighted Automata

  • Manfred Droste
  • Werner Kuich
  • Heiko Vogler

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Foundations

    1. Front Matter
      Pages 1-1
    2. Manfred Droste, Werner Kuich
      Pages 3-28
    3. Zoltán Ésik
      Pages 29-65
  3. Concepts of Weighted Recognizability

    1. Front Matter
      Pages 67-67
    2. Zoltán Ésik, Werner Kuich
      Pages 69-104
    3. Jacques Sakarovitch
      Pages 105-174
    4. Manfred Droste, Paul Gastin
      Pages 175-211
    5. Mehryar Mohri
      Pages 213-254
  4. Weighted Discrete Structures

    1. Front Matter
      Pages 255-255
    2. Ion Petre, Arto Salomaa
      Pages 257-289
    3. Juha Honkala
      Pages 291-311
    4. Zoltán Fülöp, Heiko Vogler
      Pages 313-403
    5. Ina Fichtner, Dietrich Kuske, Ingmar Meinecke
      Pages 405-450
  5. Applications

    1. Front Matter
      Pages 451-451
    2. Jürgen Albert, Jarkko Kari
      Pages 453-479
    3. George Rahonis
      Pages 481-517
    4. Christel Baier, Marcus Größer, Frank Ciesinski
      Pages 519-570
    5. Kevin Knight, Jonathan May
      Pages 571-596
  6. Back Matter
    Pages 597-608

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.


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

Editors and affiliations

  • Manfred Droste
    • 1
  • Werner Kuich
    • 2
  • Heiko Vogler
    • 3
  1. 1.Inst. InformatikUniversität LeipzigLeipzigGermany
  2. 2.Institut für DiskreteTU WienWienAustria
  3. 3.Fak. InformatikTU DresdenDresdenGermany

Bibliographic information

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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)