(Ebook) Handbook of Automata Theory Volume II Automata in Mathematics and Selected Applications by Jean-Éric Pin ISBN 9783985470020, 9783985470037, 3985470022, 3985470030

(Ebook) Handbook of Automata Theory Volume II Automata in Mathematics and Selected Applications by Jean-Éric Pin ISBN 9783985470020, 9783985470037, 3985470022, 3985470030

The Handbook of Automata Theory has its origins in the research programme AutoMathA(Automata: from Mathematics to Applications, 2005–2010), a multidisciplinaryprogramme of the European Science Foundation at the crossroads of mathematics,theoretical computer science, and applications. It is designed to provide a broadaudience of researchers and students in mathematics and computer science with a comprehensiveoverview of research in automata theory.Automata theory is one of the longest established areas in computer science. Itwas born over sixty years ago, with the seminal work of Kleene, who first formalisedthe early attempts of McCulloch and Pitts, and was originally motivated by the studyof neural networks. For many years, its main applications have been computer design,compilation of programming languages, and pattern matching. But over the last twentyyears, applications of automata theory have considerably diversified, and now includeverification methods to cope with such emerging technical needs as network security,mobile intelligent devices, and high performance computing.At the same time, the mathematical foundations of automata theory rely on moreand more advanced parts of mathematics. While only elementary graph theory andcombinatorics were required in the early sixties, new tools from non-commutativealgebra (semigroups, semirings and formal power series), logic, probability theory, andsymbolic dynamics have been successively introduced, and the latest developmentsborrow ideas from topology and geometry.It was time to gather these mathematical advances and their numerous applicationsin a reference book. The Handbook of Automata Theory is intended to serve thispurpose. It comprises thirty-nine chapters, presented in two volumes:Volume I: Theoretical foundationsVolume II: Automata in mathematics and selected applications