NEW RESULTS ON COMPUTABILITY OF RECURRENCE EQUATIONS

Abstract

Systems of uniform recurrence equations were proposed by Karp et al.13 as a mean of automatically deriving programs for parallel architectures. Extensions of this formalism are used by many authors in systolic array synthesis. The computability of a system of recurrence equations is therefore of primary importance, and is considered as the first point to be examined when trying to implement an algorithm. This paper investigates the computability of recurrence equations and especially new results obtained in this area. We first recall the definitions of computability proposed by Karp et al.,13 Rao,31 Joinnault12 and Saouter et al.32 Then we correct and generalize those results. Finally, we give a new original proof for the undecidability of computability of non-uniform, non-conditional systems of recurrence equations.