In this article we provide a refined analysis of learning in finite pa
rameter spaces using the Triggering Learning Algorithm (TLA) of Gibson
and Wexler (1994). We show that the behavior of the TLA can be modele
d exactly as a Markov chain. This Markov model allows us to (1) descri
be formally the conditions for learnability in such spaces, (2) uncove
r problematic states in addition to the local maxima described by Gibs
on and Wexler, and (3) characterize convergence times for the learning
algorithms quantitatively. In addition, we present arguments question
ing the psychological plausibility of the TLA as a learning algorithm.