On the Positivity Problem for Simple Linear Recurrence Sequences,

  • Joël Ouaknine
  • James Worrell
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8573)


Given a linear recurrence sequence (LRS) over the integers, the Positivity Problem asks whether all terms of the sequence are positive. We show that, for simple LRS (those whose characteristic polynomial has no repeated roots) of order 9 or less, Positivity is decidable, with complexity in the Counting Hierarchy.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Joël Ouaknine
    • 1
  • James Worrell
    • 1
  1. 1.Department of Computer ScienceOxford UniversityUK

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