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 ∆p2 is not equal to...

Abstract In this letter, we will clarify the reducibility of the complex-valued neural network. In the case of the complex-valued neural network, the reducibility is expressed by nπ/2 rotation-equivalence instead of sign-equivalence which Sussmann defined to show the reducibility of the real-valued neural network. In addition to the two conditions of sign-equivalence, nπ/2 rotation-equivalence ...

Two methods are used usually for to establish the collapse result for theories. They use the isolation property and the reducibility property. Early it is shown that the reducibility implies the isolation. We prove that these methods are equivalent.