Efficient Computation in Groups Via Compression

  • Markus Lohrey
  • Saul Schleimer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4649)

Abstract

We study the compressed word problem: a variant of the word problem for finitely generated groups where the input word is given by a context-free grammar that generates exactly one string. We show that finite extensions and free products preserve the complexity of the compressed word problem. Also, the compressed word problem for a graph group can be solved in polynomial time. These results allow us to obtain new upper complexity bounds for the word problem for certain automorphism groups and group extensions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Markus Lohrey
    • 1
  • Saul Schleimer
    • 2
  1. 1.Universität Stuttgart, FMIGermany
  2. 2.School of Mathematics and Statistics, Rutgers University, Mathematics Department, New Brunswick, New JerseyUSA

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