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The Compressed Word Problem for Groups

  • Book
  • © 2014

Overview

Authors:
  1. Markus Lohrey

    1. Department for Electrical Engineering and Computer Science, University of Siegen, Siegen, Germany

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  • Provides a detailed introduction into an active research area in combinatorial group theory
  • Accessible to mathematicians as well as computer scientists

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xii
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  2. Preliminaries from Theoretical Computer Science

    • Markus Lohrey
    Pages 1-26

  3. Preliminaries from Combinatorial Group Theory

    • Markus Lohrey
    Pages 27-41

  4. Algorithms on Compressed Words

    • Markus Lohrey
    Pages 43-65

  5. The Compressed Word Problem

    • Markus Lohrey
    Pages 67-85

  6. The Compressed Word Problem in Graph Products

    • Markus Lohrey
    Pages 87-113

  7. The Compressed Word Problem in HNN-Extensions

    • Markus Lohrey
    Pages 115-135

  8. Outlook

    • Markus Lohrey
    Pages 137-138

  9. Back Matter

    Pages 139-153
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Keywords

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.

Authors and Affiliations

  • Department for Electrical Engineering and Computer Science, University of Siegen, Siegen, Germany

    Markus Lohrey

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