[PDF] A Course In Formal Languages Automata And Groups eBook

Author : Ian M. Chiswell
Publisher : Springer
Page : 157 pages
File Size : 25,91 MB
Release : 2009-02-06
Category : Mathematics
ISBN : 9781848009394

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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.

Author : Ian M. Chiswell
Publisher : Springer Science & Business Media
Page : 162 pages
File Size : 37,44 MB
Release : 2008-11-14
Category : Mathematics
ISBN : 1848009402

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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.

Author : Jeffrey Shallit
Publisher : Cambridge University Press
Page : 0 pages
File Size : 39,17 MB
Release : 2009
Category : Computers
ISBN : 0521865727

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A textbook for a graduate course on formal languages and automata theory, building on prior knowledge of theoretical computer models.

Author : Peter Linz
Publisher : Jones & Bartlett Publishers
Page : 408 pages
File Size : 33,8 MB
Release : 1997
Category : Computers
ISBN :

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An Introduction to Formal Languages & Automata provides an excellent presentation of the material that is essential to an introductory theory of computation course. The text was designed to familiarize students with the foundations & principles of computer science & to strengthen the students' ability to carry out formal & rigorous mathematical argument. Employing a problem-solving approach, the text provides students insight into the course material by stressing intuitive motivation & illustration of ideas through straightforward explanations & solid mathematical proofs. By emphasizing learning through problem solving, students learn the material primarily through problem-type illustrative examples that show the motivation behind the concepts, as well as their connection to the theorems & definitions.

Author : Derek F. Holt
Publisher : Cambridge University Press
Page : 307 pages
File Size : 14,17 MB
Release : 2017-02-23
Category : Computers
ISBN : 1107152356

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A reference book discussing applications of formal language theory to group theory, particularly geometric and computational group theory.

Author : Song Y. Yan
Publisher : World Scientific
Page : 424 pages
File Size : 22,64 MB
Release : 1998
Category : Computers
ISBN : 9789810234225

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This book provides a concise and modern introduction to Formal Languages and Machine Computation, a group of disparate topics in the theory of computation, which includes formal languages, automata theory, turing machines, computability, complexity, number-theoretic computation, public-key cryptography, and some new models of computation, such as quantum and biological computation. As the theory of computation is a subject based on mathematics, a thorough introduction to a number of relevant mathematical topics, including mathematical logic, set theory, graph theory, modern abstract algebra, and particularly number theory, is given in the first chapter of the book. The book can be used either as a textbook for an undergraduate course, for a first-year graduate course, or as a basic reference in the field.

Author : S.P.Eugene Xavier
Publisher : New Age International
Page : 35 pages
File Size : 11,33 MB
Release : 2005
Category : Computational complexity
ISBN : 8122416551

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This Book Is Aimed At Providing An Introduction To The Basic Models Of Computability To The Undergraduate Students. This Book Is Devoted To Finite Automata And Their Properties. Pushdown Automata Provides A Class Of Models And Enables The Analysis Of Context-Free Languages. Turing Machines Have Been Introduced And The Book Discusses Computability And Decidability. A Number Of Problems With Solutions Have Been Provided For Each Chapter. A Lot Of Exercises Have Been Given With Hints/Answers To Most Of These Tutorial Problems.

Author : Clara Löh
Publisher : Springer
Page : 390 pages
File Size : 27,47 MB
Release : 2017-12-19
Category : Mathematics
ISBN : 3319722549

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Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.

Author : Charles C. Sims
Publisher : Cambridge University Press
Page : 624 pages
File Size : 47,68 MB
Release : 1994-01-28
Category : Mathematics
ISBN : 0521432138

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Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theoretical computer scientists will find this book useful.

Author : Stefano Crespi Reghizzi
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 37,25 MB
Release : 2009-04-03
Category : Computers
ISBN : 184882050X

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State of books on compilers The book collects and condenses the experience of years of teaching compiler courses and doing research on formal language theory, on compiler and l- guage design, and to a lesser extent on natural language processing. In the turmoil of information technology developments, the subject of the book has kept the same fundamental principles over half a century, and its relevance for theory and practice is as important as in the early days. This state of a?airs of a topic, which is central to computer science and is based on consolidated principles, might lead us to believe that the acc- panying textbooks are by now consolidated, much as the classical books on mathematics. In fact this is rather not true: there exist ?ne books on the mathematical aspects of language and automata theory, but the best books on translators are sort of encyclopaedias of algorithms, design methods, and practical know-how used in compiler design. Indeed a compiler is a mic- cosm,featuring avarietyofaspectsrangingfromalgorithmicwisdomto CPU andmemoryexploitation.Asaconsequencethetextbookshavegrowninsize, and compete with respect to their coverage of the last developments on p- gramming languages, processor architectures and clever mappings from the former to the latter.