Strong equivalence is a stronger condition for model validation than is weak equivalence. If two systems are strongly equivalent then 1) they compute the same function (i.e., they are weakly equivalent), 2) they use the same program to compute this function, and 3) this program is written in the same programming language (i.e., the two systems have the same functional architecture.)
As far as "algorithmic" approaches to cognitive science are concerned (e.g., experimental psychology, psycholinguistics), the aim of the discipline is to generate strongly equivalent theories of people. This requires collecting evidence to support the claim that a simulation uses the same procedures to solve a problem as do human subjects, as well as evidence to support the claim that a proposed architecture is primitive. It is not surprising, then, that the search for strongly equivalent theories is a formidable (but necessary) challenge for cognitive scientists.
Pylyshyn, Z.W. (1984). Computation and cognition. Cambridge, MA: MIT Press.
Functional Architecture | Weak Equivalence
Contributed by M.R.W. Dawson, November 10, 1995