SpringerBriefs in Mathematics

The Compressed Word Problem for Groups

Authors: Lohrey, Markus

  • Provides a detailed introduction into an active research area in combinatorial group theory
  • Accessible to mathematicians as well as computer scientists
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eBook $39.99
price for USA (gross)
  • ISBN 978-1-4939-0748-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-1-4939-0747-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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About this book

The Compressed Word Problem for Groups provides a detailed exposition of known results on the compressed word problem, emphasizing efficient algorithms for the compressed word problem in various groups. The author presents the necessary background along with the most recent results on the compressed word problem to create a cohesive self-contained book accessible to computer scientists as well as mathematicians. Readers will quickly reach the frontier of current research which makes the book especially appealing for students looking for a currently active research topic at the intersection of group theory and computer science. The word problem introduced in 1910 by Max Dehn is one of the most important decision problems in group theory. For many groups, highly efficient algorithms for the word problem exist. In recent years, a new technique based on data compression for providing more efficient algorithms for word problems, has been developed, by representing long words over group generators in a compressed form using a straight-line program. Algorithmic techniques used for manipulating compressed words has shown that the compressed word problem can be solved in polynomial time for a large class of groups such as free groups, graph groups and nilpotent groups. These results have important implications for algorithmic questions related to automorphism groups.

Table of contents (7 chapters)

  • Preliminaries from Theoretical Computer Science

    Lohrey, Markus

    Pages 1-26

  • Preliminaries from Combinatorial Group Theory

    Lohrey, Markus

    Pages 27-41

  • Algorithms on Compressed Words

    Lohrey, Markus

    Pages 43-65

  • The Compressed Word Problem

    Lohrey, Markus

    Pages 67-85

  • The Compressed Word Problem in Graph Products

    Lohrey, Markus

    Pages 87-113

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-1-4939-0748-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-1-4939-0747-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Compressed Word Problem for Groups
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2014
Publisher
Springer-Verlag New York
Copyright Holder
Markus Lohrey
eBook ISBN
978-1-4939-0748-9
DOI
10.1007/978-1-4939-0748-9
Softcover ISBN
978-1-4939-0747-2
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XII, 153
Number of Illustrations and Tables
27 b/w illustrations
Topics