The Orbit Problem Is in the GapL Hierarchy

  • V. Arvind
  • T. C. Vijayaraghavan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)


The Orbit problem is defined as follows: Given a matrix A εn×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 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • V. Arvind
    • 1
  • T. C. Vijayaraghavan
    • 2
  1. 1.The Institute of Mathematical SciencesChennaiIndia
  2. 2.Chennai Mathematical InstituteSiruseriIndia

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