The complexity of learning branches and strategies from queries

Abstract

We study the problems of efficiently learning infinite branches for finite state trees and winninig strategies for closed finitestate games using membership, and branch or strategy queries, respectively. We show that generally no efficient branch learning algorithm exists but we provide such algorithms for several natural cases, in particular for deadend free finite-state trees, the class of trees such that the set of infinite branches has positive measure, and several classes of modulo trees. Furthermore, we find a way to apply Angluin's results about the identification of deterministic finite automata from queries, which yields positive and negative strategy learning results, in particular, we show that the class of deadend free closed finite-state games is efficiently strategy learnable from membership and strategy queries.