On truth-table reducibility to SAT and the difference hierarchy over NP

It is shown that polynomial-time truth-table reducibility by Boolean circuits to SAT is the same as log-space truth-table reducibility via Boolean formulas to SAT and the same as log-space Turing reducibility to SAT. It is proved that a constant number of rounds of parallel queries to SAT is equivalent to one round of parallel queries. It is shown that the infinite difference hierarchy over NP is equal to Δp/2, and an oracle separating Δp/2 from the class of predicates polynomial time truth-table reducible to SAT is given