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  • Markus Lohrey
Chapter
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

We conclude this book with a few remarks about topics related to the compressed word problem for groups, which could not be covered for space reasons. In this book, we focused on the compressed word problem for groups. But it makes perfect sense to study the compressed word problem for finitely generated monoids as well. If M is a finitely generated monoid with a finite generating set Σ, then the compressed word problem for M asks whether, for given SLPs \(\mathbb{A}\) and \(\mathbb{B}\) over Σ, \(\mathsf{val}(\mathbb{A}) = \mathsf{val}(\mathbb{B})\) holds in M. As for groups, the complexity of this problem is independent of the concrete generating set.

Keywords

Polynomial Time Automorphism Group Word Problem Minimal Solution Power Circuit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Markus Lohrey 2014

Authors and Affiliations

  • Markus Lohrey
    • 1
  1. 1.Department for Electrical Engineering and Computer ScienceUniversity of SiegenSiegenGermany

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