Lower bounds for the complexity of learning half-spaces with membership queries

Exact learning of half-spaces over finite subsets of IRn from membership queries is considered. We describe the minimum set of labelled examples separating the target concept from all the other ones of the concept class under consideration. For a domain Consisting of all integer points of some polytope we give non-trivial-lower bounds on the complexity of exact identification of half-spaces. These bounds are near to known upper bounds.