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The orbit problem is in the GapL hierarchy

Author

Listed:
  • V. Arvind

    (Institute of Mathematical Sciences)

  • T. C. Vijayaraghavan

    (Chennai Mathematical Institute)

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.

Suggested Citation

  • V. Arvind & T. C. Vijayaraghavan, 2011. "The orbit problem is in the GapL hierarchy," Journal of Combinatorial Optimization, Springer, vol. 21(1), pages 124-137, January.
    • Handle: RePEc:spr:jcomop:v:21:y:2011:i:1:d:10.1007_s10878-009-9243-8
    DOI: 10.1007/s10878-009-9243-8
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