Shift Equivalence of P-finite Sequences

We present an algorithm which decides the shift equivalence problem for Pfinite 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.