A Course in Formal Languages, Automata and Groups

By: Ian M. Chiswell

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Paperback | 6 February 2009

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168 Pages

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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.

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"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)

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You Can Find This Book In

Non-Fiction Mathematics Groups & Group Theory Language & Linguistics Reference, Dictionaries & Guides Computing & I.T.Computer Science Mathematical Theory of Computation Topology Algebraic Topology Geometry Analytic Geometry

Mathematical Foundation Mathematical Logic Algebra

Preface
Grammars and Machine Recognition	p. 1
Recursive Functions	p. 21
Recursively Enumerable Sets and Languages	p. 49
Context-free Languages	p. 59
Connections with Group Theory	p. 93
Results and Proofs Omitted in the Text	p. 131
The Halting Problem and Universal Turing Machines	p. 139
Cantor's Diagonal Argument	p. 141
Solutions to Selected Exercises	p. 143
References	p. 151
Index	p. 153
Table of Contents provided by Blackwell. All Rights Reserved.

A Course in Formal Languages, Automata and Groups

At a Glance

Paperback

Industry Reviews

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How to return your order

Defective items

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