LEARNING COUNTING FUNCTIONS WITH QUERIES

We investigate the problem of learning disjunctions of counting functi ons, which are general cases of parity and module functions, with equi valence and membership queries. We prove that, for any prime number p, the class of disjunctions of integer-weighted counting functions with modulus p over the domain Z(q)(n) (or Z(n)) for any given integer q g reater than or equal to 2 is polynomial time learnable using at most n + 1 equivalence queries, where the hypotheses issued by the learner a re disjunctions of at most n counting functions with weights from Z(p) . In general, a counting function may have a composite modulus. We pro ve that, for any given integer q greater than or equal to 2, over the domain Z(2)(n), the class of read-once disjunctions of Boolean-weighte d counting functions with modulus q is polynomial-time learnable with only one equivalence query and O(n(q)) membership queries.