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A Course in Formal Languages, Automata and Groups (Universitext)by Ian Chiswell
Synopses & ReviewsPublisher Comments:Based on the author's lecture notes for an MSc course, this text combines formal language and automata theory and group theory, a thriving research area that has developed extensively over the last twentyfive years. The aim of the first three chapters is to give a rigorous proof that various notions of recursively enumerable language are equivalent. Chapter One begins with languages defined by Chomsky grammars and the idea of machine recognition, contains a discussion of Turing Machines, and includes work on finite state automata and the languages they recognise. The following chapters then focus on topics such as recursive functions and predicates; recursively enumerable sets of natural numbers; and the grouptheoretic connections of language theory, including a brief introduction to automatic groups. Highlights include: A comprehensive study of contextfree languages and pushdown automata in Chapter Four, in particular a clear and complete account of the connection between LR(k) languages and deterministic contextfree languages. A selfcontained discussion of the significant MullerSchupp result on contextfree groups. Enriched with precise definitions, clear and succinct proofs and worked examples, the book is aimed primarily at postgraduate students in mathematics but will also be of great interest to researchers in mathematics and computer science who want to learn more about the interplay between group theory and formal languages. A solutions manual is available to instructors via www.springer.com.
Synopsis:This comprehensive text uniquely presents a thorough introduction into the connections between group theory and formal languages. It also offers precise definitions, clear and succinct proofs, and an account of the MullerSchupp theorem.
Synopsis:The study of formal languages and automata has proved to be a source of much interest and discussion amongst mathematicians in recent times. This book, written by Professor Ian Chiswell, attempts to provide a comprehensive textbook for undergraduate and postgraduate mathematicians with an interest in this developing field. The first three Chapters give a rigorous proof that various notions of recursively enumerable language are equivalent. Chapter Four covers the contextfree languages, whereas Chapter Five clarifies the relationship between LR(k) languages and deterministic (contextfree languages). Chiswell's book is unique in that it gives the reader a thorough introduction into the connections between group theory and formal languages. This information, contained within the final chapter, includes work on the Anisimov and MullerSchupp theorems.
Table of ContentsPreface. Contents. 1. Grammars and Machine Recognition. 2. Recursive Functions. 3. Recursively Enumerable Sets and Languages. 4. Contextfree language. 5. Connections with Group Theory. A. Results and Proofs Omitted in the Text. B. The Halting Problem and Universal Turing Machines. C. Cantor's Diagonal Argument. D. Solutions to Selected Exercises. References. Index.
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