# Between the deterministic and non-deterministic query complexity

We consider problems that can be solved by asking certain queries. The deterministic query complexity D(P) of a problem P is the smallest number of queries needed to ask in order to find the solution (in the worst case), while the non-deterministic query complexity D_0(P) is the smallest number of queries needed to ask, in case we know the solution, to prove that it is indeed the solution (in the worst case). Equivalently, D(P) is the largest number of queries needed to find the solution in case an Adversary is answering the queries, while D_0(P) is the largest number of queries needed to find the solution in case an Adversary chooses the input. We define a series of quantities between these two values, D_k(P) is the largest number of queries needed to find the solution in case an Adversary chooses the input, and answers the queries, but he can change the input at most k times. We give bounds on D_k(P) for various problems P.

READ FULL TEXT