03750nam a22005535i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001600186072002300202082001400225100003000239245010000269264003800369300004300407336002600450337002600476338003600502347002400538490001700562505039700579520153800976650001702514650002402531650003502555650002502590650001802615650002402633650002902657650002302686650001702709650003802726650004502764650002402809650005602833650004202889710003402931773002002965776003602985830001703021856004803038912001403086999001903100952007703119978-1-84800-940-0DE-He21320180115171545.0cr nn 008mamaa110406s2009 xxk| s |||| 0|eng d a97818480094009978-1-84800-940-07 a10.1007/978-1-84800-940-02doi 4aQA174-183 7aPBG2bicssc 7aMAT0020102bisacsh04a512.22231 aChiswell, Ian M.eauthor.12aA Course in Formal Languages, Automata and Groupsh[electronic resource] /cby Ian M. Chiswell. 1aLondon :bSpringer London,c2009. aIX, 157 p. 30 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aUniversitext0 aPreface -- 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. aBased on the authorâ€™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. 0aMathematics. 0aMathematical logic. 0aCategory theory (Mathematics). 0aHomological algebra. 0aGroup theory. 0aAlgebraic topology. 0aManifolds (Mathematics). 0aComplex manifolds.14aMathematics.24aGroup Theory and Generalizations.24aMathematical Logic and Formal Languages.24aAlgebraic Topology.24aManifolds and Cell Complexes (incl. Diff.Topology).24aCategory Theory, Homological Algebra.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9781848009394 0aUniversitext40uhttp://dx.doi.org/10.1007/978-1-84800-940-0 aZDB-2-SMA c370992d370992 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK