Evaluating Matrix Circuits

Daniel König; Markus Lohrey

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arXiv · 1502.03540

Evaluating Matrix Circuits

Daniel König·Markus Lohrey

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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 $\mathsf{coRP}$, which is shown by a reduction to polynomial identity testing. Conversely, the compressed word problem for the linear group $\mathsf{SL}_3(\mathbb{Z})$ is equivalent to polynomial identity testing. 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 polynomial identity testing for skew arithmetic circuits.

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Daniel König, Markus Lohrey. 2015-02-12. Evaluating Matrix Circuits. https://arxiv.org/abs/1502.03540

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