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Handbook of Automata Theory

Handbook of Automata Theory

Volume I. Theoretical Foundations
Volume II. Automata in Mathematics and Selected Applications

Jean-Éric Pin (Université de Paris and CNRS, France)

ISBN print 978-3-98547-006-8, ISBN online 978-3-98547-506-3
DOI 10.4171/Automata
September 2021, 1608 pages, hardcover, 16.5 x 23.5 cm.
199.00 Euro

Automata theory is a subject of study at the crossroads of mathematics, theoretical computer science, and applications. In its core it deals with abstract models of systems whose behaviour is based on transitions between states, and it develops methods for the description, classification, analysis, and design of such systems.

The Handbook of Automata Theory gives a comprehensive overview of current research in automata theory, and is aimed at a broad readership of researchers and graduate students in mathematics and computer science.

Volume I is divided into three parts. The first part presents various types of automata: automata on words, on infinite words, on finite and infinite trees, weighted and maxplus automata, transducers, and two-dimensional models. Complexity aspects are discussed in the second part. Algebraic and topological aspects of automata theory are covered in the third part.

Volume II consists of two parts. The first part is dedicated to applications of automata in mathematics: group theory, number theory, symbolic dynamics, logic, and real functions. The second part presents a series of further applications of automata theory such as message-passing systems, symbolic methods, synthesis, timed automata, verification of higher-order programs, analysis of probabilistic processes, natural language processing, formal verification of programs and quantum computing.

The two volumes comprise a total of thirty-nine chapters, with extensive references and individual tables of contents for each one, as well as a detailed subject index.

Keywords: finite automata, Hopcroft's algorithm, regular languages, regular expressions, finite transducers, weighted automata, automata on infinite words, automata on trees, picture languages, algorithmic learning, descriptional complexity, Boolean circuits, synchronizing automata, road colouring problem, varieties of languages, profinite topology, descriptive set theory, equational theories, language equations, forest algebras, free groups, Stallings automata, automatic groups, self-similar groups, automatic sequences, numeration systems, Cobham's theorem, symbolic dynamics, synchronous automata, finite model theory, fractal image generation, communicating automata, model-checking, Church's problem, distributed synthesis, timed automata, recursion schemes, Markov decision processes, infinite-state systems, natural language processing, temporal logic, branching time logic, quantum finite automata