Computability of recurrence equations

This paper investigates the computability of recurrence equations. We first recall the results established by Karp et al. on the computability of systems of uniform recurrence equations, by Rao on regular iterative arrays and Joinnault's undecidability result on the computability of conditional systems of uniform recurrence equations with non bounded domain. Then we consider systems of parameterized affine recurrence equations, that is to say, systems of recurrence equations whose domains depend linearly on a size parameter and we establish that the computability of such systems is also undecidable