Distinguishing bounded reducibilities by sparse sets

Two kinds of restrictions on the power of oracle machines have arisen when considering resource-bounded reducibilities. The first restricts the underlying machine model used for reduction with respect to the number of queries allowed on each input (e.g. bounded-query reducibilities), the way the answers to the queries are to be used (e.g. conjunctive and disjunctive reducibilities), and the dependency between queries (e.g. adaptive and nonadaptive reducibilities). Comparison among reducibilities of this kind of restrictions reveals the differences among these oracle machine models. The second kind restricts the resources used by the oracle machine, usually in terms of runtime or workspace. The author studies the reducibilities defined by the first kind of restrictions, when the only resource bounded on oracle machines is the polynomial time bound. The results indicate that the relations between different reducibilities depend much on the formulations of the question