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Real Computational Universality: The Word Problem for a class of groups with infinite presentation

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Abstract

In this talk we introduce a class of groups represented as quotient groups
of some free groups generated by infinitely many elements and certain normal
subgroups. We show that the related word problem is universal in the Blum-Shub-Smale model
of computation, i.e. it has the same difficulty as the real Halting Problem.
This is the first natural example of a problem with this property.

The work has been done jointly with Martin Ziegler.


BibTeX - Entry

@InProceedings{meer_et_al:DagSemProc.06391.2,
  author =	{Meer, Klaus and Ziegler, Martin},
  title =	{{Real Computational Universality: The Word Problem for a class of groups with infinite presentation}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  pages =	{1--20},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6391},
  editor =	{Stephan Dahlke and Klaus Ritter and Ian H. Sloan and Joseph F. Traub},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2007/877},
  URN =		{urn:nbn:de:0030-drops-8773},
  doi =		{10.4230/DagSemProc.06391.2},
  annote =	{Keywords: Computational group theory, word problem, Blum-Shub-Smale model}
}

Keywords: Computational group theory, word problem, Blum-Shub-Smale model
Seminar: 06391 - Algorithms and Complexity for Continuous Problems
Issue date: 2007
Date of publication: 31.01.2007


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