The boolean hierarchy of NP-partitions
Information and Computation
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Prior results show that most bounded query hierarchies cannot contain finite gaps. For example, it is known that \mathand for all sets A \math\math\mathwhere \mathis the set of languages computable by polynomial-time Turing machines that make m nonadaptive queries to A; \math; \mathand \mathare the analogous adaptive queries classes; and \math, \math, \math, and \mathin turn are the analogous function classes. It was widely expected that these general results would extend to the remaining case -- languages computed with nonadaptive queries -- yet results remained elusive. The best known was that \math. We disprove the conjecture. In fact, \math. Thus there is a \mathhierarchy that contains a finite gap. We also make progress on the 3-tt vs. 2-tt case: \math/poly.