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Evaluating Matrix Circuits

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Computing and Combinatorics (COCOON 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9198))

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Abstract

The circuit evaluation problem (also known as the compressed word problem) for finitely generated linear groups is studied. The best upper bound for this problem is coRP, which is shown by a reduction to polynomial identity testing (PIT). Conversely, the compressed word problem for the linear group \(\mathsf {SL}_3(\mathbb {Z})\) is equivalent to PIT. In the paper, it is shown that the compressed word problem for every finitely generated nilpotent group is in \(\mathsf {DET} \subseteq {\mathsf {NC}}^2\). Within the larger class of polycyclic groups we find examples where the compressed word problem is at least as hard as PIT for skew arithmetical circuits.

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Authors and Affiliations

  1. Universität Siegen, Siegen, Germany

    Daniel König & Markus Lohrey

Authors
  1. Daniel König
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  2. Markus Lohrey
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Correspondence to Markus Lohrey .

Editor information

Editors and Affiliations

  1. Beijing University of Technology, Beijing, China

    Dachuan Xu

  2. University of New Brunswick, Fredericton, Canada

    Donglei Du

  3. University of Texas at Dallas, Richardson, USA

    Dingzhu Du

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König, D., Lohrey, M. (2015). Evaluating Matrix Circuits. In: Xu, D., Du, D., Du, D. (eds) Computing and Combinatorics. COCOON 2015. Lecture Notes in Computer Science(), vol 9198. Springer, Cham. https://doi.org/10.1007/978-3-319-21398-9_19

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  • DOI: https://doi.org/10.1007/978-3-319-21398-9_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21397-2

  • Online ISBN: 978-3-319-21398-9

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