This study in combinatorial group theory introduces the concept of automatic groups. It contains a succinct introduction to the theory of regular languages, a discussion of related topics in combinatorial group theory, and the connections between automatic groups and geometry which motivated the development of this new theory. It is of interest to mathematicians and computer scientists, and includes open problems that will dominate the research for years to come.
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5.0 out of 5 stars
From the horse's mouth,
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This review is from: Word Processing in Groups (Hardcover)
Cannon and Thurston created the theory of Automatic Groups, David Epstein was its first apostle, and Derek Holt (together with Epstein) implemented many of the algorithms, so you will not find a more qualified group of authors. While there has been a lot of work in the field since 1992, the book is still the canonical reference.
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5.0 out of 5 stars
Elegant Exposition of the Group theory, automata relationshi,
By Gabe Merton (Potsdam, NY) - See all my reviews
This review is from: Word Processing in Groups (Hardcover)
Word Processing in Groups provides a thorough yet complete exposition on the relationship between finite state automata and Group theory.
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Inside This Book
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First Sentence:
The concept of a finite state automaton has emerged as significant in many branches of human knowledge and understanding, including linguistics, computer science, philosophy, biology and mathematics, particularly in logic. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
combable group, characterizing synchronous, biautomatic structure, multiplier automata, biautomatic group, bounded length difference, nearby basepoints, asynchronous automatic structure, characterizing asynchronous, partial deterministic automaton, quadratic isoperimetric inequality, bounded cochain, second outgoing edges, one accept state, slanting section, geodesic string, graph geodesic, unique accept state, positive braid, asynchronous automaton, maximal tail, partial automaton, word hyperbolic groups, automatic groups, isoperimetric function Key Phrases - Capitalized Phrases (CAPs): (learn more)
Axiom Checking, The Basic Seifert Fibre Space, Thurston's Conjecture, Fitting Pieces Together, Generators of Differing Lengths, Geometrically Finite Groups of Hyperbolic Isometries, Groups As Languages, John Sullivan, Naive Algorithm, Simply Starred Languages, The Braid Group Is Automatic, Taking the Problem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The concept of a finite state automaton has emerged as significant in many branches of human knowledge and understanding, including linguistics, computer science, philosophy, biology and mathematics, particularly in logic. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
combable group, characterizing synchronous, biautomatic structure, multiplier automata, biautomatic group, bounded length difference, nearby basepoints, asynchronous automatic structure, characterizing asynchronous, partial deterministic automaton, quadratic isoperimetric inequality, bounded cochain, second outgoing edges, one accept state, slanting section, geodesic string, graph geodesic, unique accept state, positive braid, asynchronous automaton, maximal tail, partial automaton, word hyperbolic groups, automatic groups, isoperimetric function Key Phrases - Capitalized Phrases (CAPs): (learn more)
Axiom Checking, The Basic Seifert Fibre Space, Thurston's Conjecture, Fitting Pieces Together, Generators of Differing Lengths, Geometrically Finite Groups of Hyperbolic Isometries, Groups As Languages, John Sullivan, Naive Algorithm, Simply Starred Languages, The Braid Group Is Automatic, Taking the Problem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 6
books:
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44
books
cite this book:
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- Elements Of Algebraic Topology by James R. Munkres in Back Matter
- Fundamentals of Abstract Analysis by Andrew Gleason in Back Matter
- Advanced Calculus, Revised Edition by Loomis in Back Matter
- Geometric Measure Theory (Classics in Mathematics) by Herbert Federer in Back Matter
- Differential Equations by Ray Redheffer in Back Matter
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- Algorithmic Problems in Groups and Semigroups (Trends in Mathematics) by Jean-Camille Birget on page 85, page 191, and page 215
- Computational and Geometric Aspects of Modern Algebra (London Mathematical Society Lecture Note Series) by Michael Atkinson on page 37, page 76, and page 189
- Groups St Andrews 2005: Volume 1 (London Mathematical Society Lecture Note Series) by C. M. Campbell on page 351, and page 462
- Geometric Group Theory Down Under: Proceedings of a Special Year in Geometric Group Theory, Canberra, Australia, 1996 ([De Gruyter Proceedings in Mathematics]) by John Cossey on page 146, and page 279
- Groups-Korea '94: Proceedings of the International Conference, Held at Pusan National University, Pusan, Korea, August 18-25, 1994 ([De Gruyter Proceedings in Mathematics]) by A. C. Kim on page 66, and Back Matter
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