عنوان

The compressed word problem for groups /

(Number (ISBN

1493907484 (electronic bk.)

(Number (ISBN

9781493907489 (electronic bk.)

Erroneous ISBN

1493907476 (print)

Erroneous ISBN

9781493907472

Erroneous ISBN

9781493907472 (print)

Number

dltt

Title Proper

The compressed word problem for groups /

General Material Designation

[Book]

First Statement of Responsibility

Markus Lohrey

Specific Material Designation and Extent of Item

1 online resource (xii, 153 pages) :

Other Physical Details

illustrations.

Series Title

SpringerBriefs in Mathematics,

ISSN of Series

2191-8198

Text of Note

Includes bibliographical references and index

Text of Note

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

0

Text of Note

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

International Standard Book Number

9781493907472

Group theory.

Word problems (Mathematics)

Analysis.

Group Theory and Generalizations.

Mathematics.

Topological Groups, Lie Groups.

MAT-- 002040

MAT002010

PBG

Number

Edition

Class number

Lohrey, Markus

Ohio Library and Information Network.

Date of Transaction

20201222074646.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

270410

Y