A probabilistic model for the degree of the cancellation polynomial in Gosper's Algorithm

Abstract

Milenkovic and Compton in 2002 gave an analysis of the run time of Gosper's algorithm applied to a random input. The main part of this was an asymptotic analysis of the random degree of the cancellation polynomial c(k) under various stipulated laws for the input. Their methods use probabilistic transform techniques. Here, a more general classof input distributions is considered, and limit laws of the type proved by Milenkovic and Compton are shown to follow from a general functional central limit theorem. The methods herein are probabilistic and elementary and may be used to compute the means of the limiting distributions.