Shift Equivalence of P-finite Sequences

Abstract

We present an algorithm which decides the shift equivalence problem for P-finite sequences. A sequence is called P-finite if it satisfies a homogeneous linear recurrence equation with polynomial coefficients. Two sequences are called shift equivalent if shifting one of the sequences $s$ times makes it identical to the other, for some integer $s$. Our algorithm computes, for any two P-finite sequences, given via recurrence equation and initial values, all integers $s$ such that shifting the first sequence $s$ times yields the second.