  Let W~ be an affine Weyl group, and let C be a left, right, or two-sided
Kazhdan--Lusztig cell in W~. Let Reduced (C) be the set of all reduced
expressions of elements of C, regarded as a formal language in the sense of the
theory of computation. We show that Reduced (C) is a regular language. Hence
the reduced expressions of the elements in any Kazhdan--Lusztig cell can be
enumerated by a finite state automaton.
