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Book Cover
Author Epstein, D. B. A., author.

Title Word Processing in Groups / David B.A. Epstein
Published Boca Raton, FL : A K Peters/CRC Press, 1992
Online access available from:
ProQuest Ebook Central    View Resource Record  


Description 1 online resource
Contents Cover; Half Title; Dedication; Title Page; Copyright Page; Contents; Preface; I: An Introduction to Automatic Groups; 1 Finite State Automata, Regular Languages and Predicate Calculus; 1.1 Languages and Regular Languages; 1.2 Finite State Automata; 1.3 Simply Starrep Languages; 1.4 Predicate Calculus and Regular Languages; 2 Automatic Groups; 2.1 Groups As Languages; 2.2 Cayley Graphs and Isoperimetric Inequalities; 2.3 Automatic Groups: Definition; 2.4 lnvariance under Change of Generators; 2.5 Improving the Automatic Structure; 3 Quasigeodesics, Pseudoisometries and Combings
10 Higher-Dimensional Isoperimetric Inequalities10.1 Cell Complexes and Lipschitz Maps; 10.2 Estimates for Cell Complexes; 10.3 Combable Groups and Riemannian Manifolds; 10.4 The Special Linear Groups; 11 Geometrically Finite Groups; 11.1 Groupoids; 11. 2 Generators of Differing Lengths; 11.3 Geodesics and Horoballs; 11.4 Geometrically Finite Groups of Hyperbolic Isometries; 12 Three-Dimensional Manifolds; 12.1 Taking the Problem to Pieces; 12.2 The Basic Seifert Fibre Space; 12.3 Fitting Pieces Together along the Boundaries; 12.4 The Automatic Structure on a Three-Manifold; Bibliography
3.1 Metric Spaces, Path Metrics and Geodesics3.2 Shortest Strings; 3.3 Pseudoisometries; 3.4 Applications to Fundamental Groups; 3.5 Counterexample to the Use of Shortest Strings; 3.6 Combable Groups; 4 Abelian and Euclidean Groups; 4.1 General Results; 4.2 Euclidean Groups are Biautomatic; 4.3 Abelian Groups and Shortlex; 4.4 A Euclidean Counterexample; 5 Finding the Automatic Structure: Theory; 5.1 Axiom Checking; 5.2 A Naive Algorithm; 6 Finding the Automatic Structure: Practical Methods; 6.1 Semigroups and Specialized Axioms; 6.2 The Knuth-Bendix Procedure
6.3 Knuth-Bendix and Word Differences7 Asynchronous Automatic Groups; 7.1 Asynchronous Automata; 7.2 Asynchronous Automatic Groups: Definition; 7.3 Properties of Asynchronous Automatic Groups; 7.4 Asynchronous but not synchronous; 8 Nilpotent Groups; 8.1 The Heisenberg Group; 8.2 Nilpotent Groups Are Not Automatic; 8.3 Regular Subgroups and Nilpotency; II: Topics in the Theory of Automatic Groups; 9 Braid Groups; 9.1 The Braid Group and the Symmetric Group; 9.2 Canonical Forms; 9.3 The Braid Group Is Automatic; 9.4 The Conjugacy Problem; 9.5 Complexity Issues
Summary "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."--Provided by publisher
Analysis Formal languages
Group theory
Sequential machine theory
Bibliography Includes bibliographical references and index
Notes Online resource; title from PDF title page (EBSCO, viewed May 23, 2018)
Subject Formal languages
Group theory
Sequential machine theory
Form Electronic book
ISBN 1439865698