This paper shows how to learn general, Finite State Machine representations of activities that function as recognizers of previously unseen instances of activities. The central problem is to tell which differences between instances of activities are unimportant and may be safely ignored for the purpose of learning generalized representations of activities. We develop a novel way to find the "essential parts" of activities by a greedy kind of multiple sequence alignment, and a method to transform the resulting alignments into Finite State Machine that will accept novel instances of activities with high accuracy.