Handbook of Weighted Automata

ISBN-13: 9783642014918 / Angielski / Twarda / 2009 / 628 str.

Manfred Droste; Werner Kuich; Heiko Vogler

Opis

The purpose of this Handbook is to highlight both theory and applications of weighted automata. Weighted ?nite automata are classical nondeterministic ?nite 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 neededforthis, ortheprobabilityorreliabilityofitssuccessful execution. The behavior of weighted ?nite automata can then be considered as the function (suitably de?ned) associating with each word the weight of its execution. Clearly, weights can also be added to classical automata with in?nite 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 f- lowing 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 "pro?t" and then be interested in the maximal pro't realized, correspondingly, by a given word.

Recenzje

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)

Spis treści

Foundations.- Semirings and Formal Power Series.- Fixed Point Theory.- Concepts of Weighted Recognizability.- Finite Automata.- Rational and Recognisable Power Series.- Weighted Automata and Weighted Logics.- Weighted Automata Algorithms.- Weighted Discrete Structures.- Algebraic Systems and Pushdown Automata.- Lindenmayer Systems.- Weighted Tree Automata and Tree Transducers.- Traces, Series-Parallel Posets, and Pictures: A Weighted Study.- Applications.- Digital Image Compression.- Fuzzy Languages.- Model Checking Linear-Time Properties of Probabilistic Systems.- Applications of Weighted Automata in Natural Language Processing.