Abstract
The Orbit problem is defined as follows: Given a matrix A∈ℚn×n and vectors x,y∈ℚn, does there exist a non-negative integer i such that A i x=y. This problem was shown to be in deterministic polynomial time by Kannan and Lipton (J. ACM 33(4):808–821, 1986). In this paper we place the problem in the logspace counting hierarchy GapLH. We also show that the problem is hard for C=L with respect to logspace many-one reductions.
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A preliminary version of this paper was presented at the COCOON 2008 conference (Arvind and Vijayaraghavan 2008).
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Arvind, V., Vijayaraghavan, T.C. The orbit problem is in the GapL hierarchy. J Comb Optim 21, 124–137 (2011). https://doi.org/10.1007/s10878-009-9243-8
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DOI: https://doi.org/10.1007/s10878-009-9243-8