Journal of Combinatorial Optimization

, Volume 21, Issue 1, pp 124–137 | Cite as

The orbit problem is in the GapL hierarchy

  • V. Arvind
  • T. C. Vijayaraghavan


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.


Orbit problem Linear algebra Parallel complexity Logspace counting classes Parallel algorithm 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Institute of Mathematical SciencesChennaiIndia
  2. 2.Chennai Mathematical InstituteSiruseriIndia

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