Abstract
The Orbit problem is defined as follows: Given a matrix A εℚn×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 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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Arvind, V., Vijayaraghavan, T.C. (2008). The Orbit Problem Is in the GapL Hierarchy. In: Hu, X., Wang, J. (eds) Computing and Combinatorics. COCOON 2008. Lecture Notes in Computer Science, vol 5092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69733-6_17
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DOI: https://doi.org/10.1007/978-3-540-69733-6_17
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