The Orbit Problem Is in the GapL Hierarchy

Authors:
V. Arvind;T. C. Vijayaraghavan
Affiliations:
The Institute of Mathematical Sciences, Chennai, India 600 113;Chennai Mathematical Institute, Siruseri, India 603 103
Venue:
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Year:
2008

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Abstract

The Orbit problemis defined as follows: Given a matrix A茂戮驴茂戮驴n×nand vectors x,y茂戮驴茂戮驴n, does there exist a non-negative integer isuch that Aix= 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.