The orbit problem is in the GapL hierarchy

V. Arvind () and T. C. Vijayaraghavan ()
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V. Arvind: Institute of Mathematical Sciences
T. C. Vijayaraghavan: Chennai Mathematical Institute

Journal of Combinatorial Optimization, 2011, vol. 21, issue 1, No 8, 124-137

Abstract: Abstract The Orbit problem is defined as follows: Given a matrix A∈ℚn×n and vectors x,y∈ℚ n , 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.

Keywords: Orbit problem; Linear algebra; Parallel complexity; Logspace counting classes; Parallel algorithm (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10878-009-9243-8

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