- Full Description
Weighted finite automata are classical nondeterministic finite automata in which the transitions carry weights. These weights may model, for example, the cost involved when executing a transition, the resources or time needed for this, or the probability or reliability of its successful execution. Weights can also be added to classical automata with infinite state sets like pushdown automata, and this extension constitutes the general concept of weighted automata. Since their introduction in the 1960s they have stimulated research in related areas of theoretical computer science, including formal language theory, algebra, logic, and discrete structures. Moreover, weighted automata and weighted context-free grammars have found application in natural-language processing, speech recognition, and digital image compression. This book covers all the main aspects of weighted automata and formal power series methods, ranging from theory to applications. The contributors are the leading experts in their respective areas, and each chapter presents a detailed survey of the state of the art and pointers to future research. The chapters in Part I cover the foundations of the theory of weighted automata, specifically addressing semirings, power series, and fixed point theory. Part II investigates different concepts of weighted recognizability. Part III examines alternative types of weighted automata and various discrete structures other than words. Finally, Part IV deals with applications of weighted automata, including digital image compression, fuzzy languages, model checking, and natural-language processing. Computer scientists and mathematicians will find this book an excellent survey and reference volume, and it will also be a valuable resource for students exploring this exciting research area.
- Table of Contents
Table of Contents
- Part I, Foundations: Semirings and Formal Power Series.
- Fixed Point Theory. Part II, Concepts of Weighted Recognizability: Finite Automata.
- Rational and Recognisable Power Series.
- Weighted Automata and Weighted Logics.
- Weighted Automata Algorithms. Part III, 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. Part IV, Applications: Digital Image Compression.
- Fuzzy Languages.
- Model Checking Linear
- Time Properties of Probabilistic Systems.
- Applications of Weighted Automata in Natural Language Processing. Index.
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