Restricted information from nonadaptive queries to NP

We investigate classes of sets that can be decided by bounded truth-table reductions to an NP set in which evaluators do not have full access to the answers to the queries but get only restricted information such as the number of queries that are in the oracle set or even just this number modulo m, for some m⩾2. We also investigate the case in which evaluators are nondeterministic. We locate all these classes within levels of the Boolean hierarchy, which allows us to compare the complexity of such classes. Our results show the various degrees to which the power of P or NP evaluators are affected as the restricted information that the evaluators get from the answers to the queries produced by generators is changed