On the Positivity Problem for Simple Linear Recurrence Sequences

Abstract

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.

arXiv admin note: substantial text overlap with arXiv:1307.2779