Can access to a specific type of computational oracle enhance the power of exact learning algorithms? This study investigates the learnability of representation classes within Angluin's exact learning model, exploring the impact of providing the learner with access to an oracle in the complexity class Σp2. This research explores different query types. Specifically, the authors consider three learning scenarios: equivalence queries, equivalence and membership queries, and membership queries only. For each of these scenarios, the study demonstrates that polynomial query complexity already implies polynomial-time learnability. This implication holds provided that the learner has access to a Σp2 oracle. As a consequence of this finding, boolean circuits are shown to be polynomial-time learnable with equivalence queries when aided by a Σp2 oracle. This result has significant implications for the field of computational learning theory, expanding the understanding of the power and limitations of different learning models and oracle-assisted computation. The additional power makes learning significantly easier.
This research is relevant to the International Journal of Foundations of Computer Science due to its focus on the theoretical foundations of learning and computation. The paper addresses questions about the power of oracles in exact learning models, aligning with the journal's emphasis on the mathematical and logical underpinnings of computer science.