  We give several modifications of the Goulden-Jackson Cluster method for
finding generating functions for words avoiding a given set of forbidden words.
Our modifications include functions which can take into account various
'weights' on words, including single letter probability distributions, double
letter (i.e. pairwise) probability distributions, and triple letter probability
distributions. We also describe an alternative, recursive approach to finding
such generating functions. We describe Maple implementations of the various
modifications. The accompanying Maple package is available at the website for
this paper.
