Hierarchies of probabilistic and team FIN-learning

A FIN-learning machine M receives successive values of the function f it is learning and at some moment outputs a conjecture which should be a correct index of f. FIN learning has 2 extensions: (1) If M ips fair coins and learns a function with certain probability p, we have FIN hpi-learning. (2) When n machines simultaneously try to learn the same function f and at least k of these machines output correct indices of f , we have learning by a k; n]FIN team. Sometimes a team or a probabilistic learner can simulate another one, if their probabilities p 1 ; p 2 (or team success ratios k 1 =n 1 ; k 2 =n 2) are close enough DKV92a, DK96]. On the other hand, there are cut-points r which make simulation of FIN hp 2 i by FIN hp 1 i impossible whenever p 2 r < p 1. Cut-points above 10=21 are known DK96]. We show that the problem for given k i ; n i to determine whether k 1 ; n 1 ]FIN k 2 ; n 2 ]FIN is algorithmically solvable. The set of all FIN cut-points is shown to be well-ordered and recursive. Asymmet-ric teams are introduced and used as both a tool to obtain these results , and are of interest in themselves. The framework of asymmetric teams allows us to characterize intersections k 1 ; n 1 ]FIN \k 2 ; n 2 ]FIN, 1 Based on two conference papers: AFS97] and AAF + 97]. 1 Hence, we can compare the learning power of traditional FIN-teams k; n]FIN as well as all kinds of their set-theoretic combinations.