5 research outputs found
Evaluating Matrix Circuits
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 , which is shown by a reduction to polynomial
identity testing. Conversely, the compressed word problem for the linear group
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 . 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
Presentations: from Kac-Moody groups to profinite and back
We go back and forth between, on the one hand, presentations of arithmetic
and Kac-Moody groups and, on the other hand, presentations of profinite groups,
deducing along the way new results on both