We continue the study of robust reductions initiated by Gavaldà and Balcázar. In particular, a 1991 paper of Gavaldà and Balcázar  claimed an optimal separation between the power of robust and nondeterministic strong reductions. Unfortunately, their proof is invalid. We re-establish their theorem.
Generalizing robust reductions, we note that robustly strong reductions are built from two restrictions, robust underproductivity and robust overproductivity, both of which have been separately studied before in other contexts. By systematically analyzing the power of these reductions, we explore the extent to which each restriction weakens the power of reductions. We show that one of these reductions yields a new, strong form of the Karp-Lipton Theorem.
KeywordsTuring Machine Strong Reduction Language Transformation Polynomial Hierarchy Downward Closure
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