The compressed word problem for groups [electronic resource] / Markus Lohrey.
2014
QA63
Linked e-resources
Linked Resource
Online Access
Details
Title
The compressed word problem for groups [electronic resource] / Markus Lohrey.
Author
Lohrey, Markus, author.
ISBN
9781493907489 electronic book
1493907484 electronic book
9781493907472
1493907484 electronic book
9781493907472
Published
New York, NY : Springer, 2014.
Language
English
Description
1 online resource (xii, 153 pages) : illustrations.
Item Number
10.1007/978-1-4939-0748-9 doi
Call Number
QA63
Dewey Decimal Classification
512.2
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Description based on online resource; title from PDF title page (SpringerLink, viewed April 17, 2014).
Series
SpringerBriefs in mathematics, 2191-8198
Linked Resources
Online Access
Record Appears in
Online Resources > Ebooks
All Resources
All Resources
Table of Contents
1. Preliminaries from Theoretical Computer Science
2. Preliminaries from Combinatorial Group Theory
3. Algorithms on Compressed Words
4. The Compressed Word Problem
5. The Compressed Word Problem in Graph Products
6. The Compressed Word Problem in HNN-Extensions
7.Outlook.
2. Preliminaries from Combinatorial Group Theory
3. Algorithms on Compressed Words
4. The Compressed Word Problem
5. The Compressed Word Problem in Graph Products
6. The Compressed Word Problem in HNN-Extensions
7.Outlook.