Intrinsic Complexity of Partial Learning

Abstract

A partial learner in the limit [ 16 ], given a representation of the target language (a text), outputs a sequence of conjectures, where one correct conjecture appears infinitely many times and other conjectures each appear a finite number of times. Following [ 5 , 14 ], we define intrinsic complexity of partial learning, based on reducibilities between learning problems. Although the whole class of recursively enumerable languages is partially learnable (see [ 16 ]) and, thus, belongs to the complete learnability degree, we discovered a rich structure of incomplete degrees, reflecting different types of learning strategies (based, to some extent, on topological structures of the target language classes). We also exhibit examples of complete classes that illuminate the character of the strategies for partial learning of the hardest classes.