A New Abstract Combinatorial Dimension for Exact Learning via Queries

We introduce an abstract model of exact learning via queries that can be instantiated to all the query learning models currently in use, while being closer to them than previous uniicatory attempts. We present a characterization of those Boolean function classes learnable in this abstract model, in terms of a new combinatorial notion that we introduce, the abstract identiication dimension. Then we prove that the particular-ization of our notion to speciic known protocols such as equivalence, membership, and membership and equivalence queries results in exactly the same combinatorial notions currently known to characterize learning in these models, such as strong consistency dimension, extended teaching dimension, and certiicate size. Our theory thus fully uniies all these characterizations. For models enjoying a speciic property that we identify, the notion can be simpliied while keeping the same characterizations. From our results we can derive combinatorial characterizations of all those other models for query learning proposed in the literature. We can also obtain the rst polynomial-query learning algorithms for speciic interesting problems such as learning DNF with proper subset and superset queries.