On the parallel complexity of solving recurrence equations

Abstract

We show that recurrence equations, even the simple ones, are not likely to admit fast parallel algorithms, i.e., not likely to be solvable in polylogarithmic time using a polynomial number of processors. We also look at a restricted class of recurrence equations and show that this class is solvable in O(log2 n) time, but not likely in O(log n) time.