On Truth-Table Reducibility to SAT

We show that polynomial time truth-table reducibility via Boolean circuits to SAT is the same as logspace truth-table reducibility via Boolean formulas to SAT and the same as logspace Turing reducibility to SAT. In addition, we prove that a constant number of rounds of parallel queries to SAT is equivalent to one round of parallel queries. We give an oracle relative to which Δ2p is not equal to the class of predicates polynomial time truth-table reducible to SAT.

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