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A Course in Formal Languages, Automata and Groups

  • Textbook
  • © 2009

Overview

Authors:
  1. Ian M. Chiswell

    1. Queen Mary, Department of Pure Mathematics, University of London, London, United Kingdom

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  • Most books on formal languages and automata are written for undergraduates in computer science; in contrast, this book provides a rigorous text aimed at the postgraduate-level mathematician with precise definitions and clear and succinct proofs.
  • The book examines the interplay between group theory and formal languages, and is the first to include an account of the significant Muller-Schupp theorem.
  • Includes a clear account of deterministic context-free languages and their connection with LR(k) grammars.
  • A complete solutions manual is available to lecturers via the web.
  • Includes supplementary material: sn.pub/extras
  • Request lecturer material: sn.pub/lecturer-material

Part of the book series: Universitext (UTX)

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Table of contents (5 chapters)

  1. Front Matter

    Pages 1-7
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  2. Grammars and Machine Recognition

    • Ian M. Chiswell
    Pages 1-20

  3. Recursive Functions

    • Ian M. Chiswell
    Pages 1-27

  4. Recursively Enumerable Sets and Languages

    • Ian M. Chiswell
    Pages 1-10

  5. Context-free Languages

    • Ian M. Chiswell
    Pages 1-33

  6. Connections with Group Theory

    • Ian M. Chiswell
    Pages 1-37

  7. Back Matter

    Pages 1-27
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Keywords

About this book

This book is based on notes for a master’s course given at Queen Mary, University of London, in the 1998/9 session. Such courses in London are quite short, and the course consisted essentially of the material in the ?rst three chapters, together with a two-hour lecture on connections with group theory. Chapter 5 is a considerably expanded version of this. For the course, the main sources were the books by Hopcroft and Ullman ([20]), by Cohen ([4]), and by Epstein et al. ([7]). Some use was also made of a later book by Hopcroft and Ullman ([21]). The ulterior motive in the ?rst three chapters is to give a rigorous proof that various notions of recursively enumerable language are equivalent. Three such notions are considered. These are: generated by a type 0 grammar, recognised by a Turing machine (deterministic or not) and de?ned by means of a Godel ¨ numbering, having de?ned “recursively enumerable” for sets of natural numbers. It is hoped that this has been achieved without too many ar- ments using complicated notation. This is a problem with the entire subject, and it is important to understand the idea of the proof, which is often quite simple. Two particular places that are heavy going are the proof at the end of Chapter 1 that a language recognised by a Turing machine is type 0, and the proof in Chapter 2 that a Turing machine computable function is partial recursive.

Reviews

From the reviews:

"This short work by Chiswell … covers formal languages, automata theory, and the word problem in group theory. This content is bound together by the unifying theme of what is known as Church’s thesis, which states that any desirable definition of computability should coincide with recursiveness. … Several appendixes serve as homes for … distracting proofs of results needed in the main body of the text, or for solutions to selected instances of the abundant exercises. Summing Up: Recommended. Academic readers, upper-division undergraduates through researchers/faculty." (F. E. J. Linton, Choice, Vol. 46 (11), 2009)

Authors and Affiliations

  • Queen Mary, Department of Pure Mathematics, University of London, London, United Kingdom

    Ian M. Chiswell

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