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Rene Denfeld: IMG Powell’s Q&A: Rene Denfeld



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A Course in Formal Languages, Automata and Groups (Universitext)

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A Course in Formal Languages, Automata and Groups (Universitext) Cover

 

Synopses & Reviews

Publisher 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 twenty-five 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 group-theoretic connections of language theory, including a brief introduction to automatic groups. Highlights include: A comprehensive study of context-free languages and pushdown automata in Chapter Four, in particular a clear and complete account of the connection between LR(k) languages and deterministic context-free languages. A self-contained discussion of the significant Muller-Schupp result on context-free 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 Muller-Schupp 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 context-free languages, whereas Chapter Five clarifies the relationship between LR(k) languages and deterministic (context-free 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 Muller-Schupp theorems.

Table of Contents

Preface.- Contents.- 1. Grammars and Machine Recognition.- 2. Recursive Functions.- 3. Recursively Enumerable Sets and Languages.- 4. Context-free 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.

Product Details

ISBN:
9781848009394
Author:
Chiswell, Ian
Publisher:
Springer
Editor:
Axler, Sheldon
Editor:
Capasso, Vincenzo
Author:
Chiswell, Ian M.
Subject:
Logic
Subject:
Group Theory
Subject:
Algebra - General
Subject:
Machine Theory
Subject:
Muller-Schupp Theorem
Subject:
Automata
Subject:
Formal Language
Subject:
recursive function
Subject:
Word problem
Subject:
Group Theory and Generalizations
Subject:
Mathematical Logic and Formal Languages
Subject:
Algebraic topology
Subject:
Manifolds and Cell Complexes (incl. Diff.Topology)
Subject:
Category Theory, Homological Algebra <P>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
Subject:
Mathematics-Logic and Philosophy
Subject:
Algebra - Abstract
Subject:
Category Theory, Homological Algebra
Copyright:
Edition Description:
2009
Series:
Universitext
Publication Date:
20081216
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
166
Dimensions:
235 x 155 mm

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A Course in Formal Languages, Automata and Groups (Universitext) New Trade Paper
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$56.95 In Stock
Product details 166 pages Springer - English 9781848009394 Reviews:
"Synopsis" by , 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 Muller-Schupp theorem.
"Synopsis" by , 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 context-free languages, whereas Chapter Five clarifies the relationship between LR(k) languages and deterministic (context-free 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 Muller-Schupp theorems.
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