The Orbit problem is defined as follows: Given a matrix A ∈ Q~(n×n) and vectors x,y ∈ Q~n, does there exist a non-negative integer i such that A~ix = y. This problem was shown to be in deterministic polynomial time by Kannan and Lipton in [7]. In this paper we put the problem in the logspace counting hierarchy GapLH. We also show that the problem is hard for C=L.
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