Form Invariance and Implicit Parallelism

Holland's schema theorem (an inequality) may be viewed as an attempt to understand genetic search in terms of a coarse graining of the state space. Stephens and Waelbroeck developed that perspective, sharpening the schema theorem to an equality. Of particular interest is a “form invariance” of their equations; the form is unchanged by the degree of coarse graining. This paper establishes a similar form invariance for the more general model of Vose et al. and uses the attendant machinery as a springboard for an interpretation and discussion of implicit parallelism.