The orbit problem is in the GapL hierarchy
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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.
KeywordsOrbit problem Linear algebra Parallel complexity Logspace counting classes Parallel algorithm
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- Damm C (1991) DET=L#L. Informatik-Preprint 8, Fachbereich Informatik der Humboldt-Universitat zu Berlin Google Scholar
- Hoang TM, Thierauf T (2005) The complexity of the inertia and some closure properties of GapL. In: Proceedings of 20th IEEE conference on computational complexity, pp 28–37 Google Scholar
- Toda S (1991) Counting problems computationally equivalent to computing the determinant. Technical report 91-07, Department of Computer Science, University of Electro-Communications, Tokyo, Japan Google Scholar
- Vijayaraghavan TC (2008) Classifying certain algebraic problems using logspace counting classes. PhD Thesis, Institute of Mathematical Sciences, Chennai, India. http://www.cmi.ac.in/~vijay/thesis.html
- Vinay V (1991) Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits. In: CCC’91: Proceedings of 6th structure in complexity theory conference, pp 270–284 Google Scholar