The Complexity of Learning Branches and Strategies from Queries

The problems of learning strategies for closed infinite games (as a model for learning process controllers) and of learning infinite branches of computable trees have been introduced in inductive inference. We study the complexity of these problems in a query learning model for closed games and trees represented by deterministic finite automata. We show that already for finite-state trees, which are just the one-player specialization of the closed two-person games, branches are generally not learnable from polynomially many branch and membership queries. However, the class of deadend free finite-state trees is efficiently branch learnable from branch and membership queries, while only one of these query types does not suffice. This class also witnesses that the identification problem is generally harder than the strategy learning problem. Moreover, we investigate trees such that the set of all infinite branches has non-zero measure, and modulo trees, which are based on number theoretic..