In this post I will summarize Chapter 4 of Niyogi (1998) The Informational Complexity of Learning. In it, Niyogi emphasizes the importance of going beyond theoretical learnability when analyzing a grammatical paradigm. "One also needs to quantify the sample complexity of the learning problem, i.e., how many examples does the learning algorithm need to see in order to be able to identify the target grammar with high confidence."
He sets his sights upon the Triggering Learning Algorithm, put forth by Gibson and Wexler as a learning scheme for the grammatical "parameters" within the Chomskyan Principles and Parameters framework. For those unfamiliar with the background, this is a theory of language that posits a Universal Grammar underlying all natural languages (the principles), and then a finite set of variable parameters which account for the differences among languages. The "parameter setting" is really the sole learning task for the developing child on this account.
I think that in the beginning, this theory was put forth in an effort to address the supposed "poverty of the stimulus," with the hope that the resulting learning problem would be tractable, even easy. Niyogi, however, manages to demonstrate that Gibson and Wexler's assumption of the existence of "local triggers," i.e. a path through the parameter-setting space from the initial hypothesis to the target, is not even sufficient to guarantee learnability at all (though it was believed sufficient by Gibson and Wexler), much less tractability. He further demonstrated the surprising theorem that, for all its carefully thought out design, the Triggering Learning Algorithm is less optimal than a random walk on the parameter space!
At the time of Niyogi's writing, he judged that the Triggering Learning Algorithm was a preferred explanation of language learning in psycholinguistics. His results should really have killed it, but as far as I can see they have had no such effect. In fact, Google Scholar finds only 12 literature citations of his entire book, most of which are due to the author himself. This is hardly a flurry of activity; only one other author writing on problems of natural language learning appears to be among the citations.