In Learning in the Limit and Non{uniform (; ) { Learning

We compare the two most common types of success criteria for learning processes. The (;) criterion employed in the PAC model and its many variants and extensions, and the identiication in the limit criterion that is used in inductive inference models. By applying common techniques from the theory of Probability, and a stochastic variant of Rissanen's MDL principle, we demonstrate close connections between these two types of learnability notions. We also show that, once computability issues are set aside, stochastic identiication in the limit is intimately related to the countability of a concept class.