In XCS, the match set is not limited in size. It can be as big as there are matching classifiers. In practice, the size is self-limiting, since XCS inherently tends to distribute resources (classifiers) evenly over the various niches of the environment.

In the traditional classifier system, Holland felt that a finite match set would tend to induce default hierarchies among the classifiers. I investigated this in a paper in Complex Systems (vol. 2, no. 6, p. 705, 1988) and found (1) performance declines as the match set size goes from unlimited to five members; and (2) no default hierarchies occur. These results, and others in that paper, were an early inducement to me to begin modifying the traditional model.

As for the message list, I have as yet done no experiments with XCS that use a message list (of internally posted messages). When I do, the list will probably be finite in size, say one internal message. See the second from last paragraph in Section 5.2 of the present paper, and my EC paper called "ZCS: A zeroth level classifier system", for thoughts along this line. In any case, the match set will continue to be unlimited.

(Nov 29, 1996)

In traditional Classifier Systems, strength is also used to determine which matched classifiers are allowed to post their messages to M if the size of the message list is less than the number of matched classifiers. How does XCS handle this?