A Course in Formal Languages, Automata and Groups [electronic resource] / by Ian M. Chiswell.
Contributor(s): SpringerLink (Online service)Material type: TextSeries: Universitext: Publisher: London : Springer London, 2009Description: IX, 157 p. 30 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9781848009400Subject(s): Mathematics | Mathematical logic | Category theory (Mathematics) | Homological algebra | Group theory | Algebraic topology | Manifolds (Mathematics) | Complex manifolds | Mathematics | Group Theory and Generalizations | Mathematical Logic and Formal Languages | Algebraic Topology | Manifolds and Cell Complexes (incl. Diff.Topology) | Category Theory, Homological AlgebraAdditional physical formats: Printed edition:: No titleDDC classification: 512.2 LOC classification: QA174-183Online resources: Click here to access online
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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.
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.