The power of adaptiveness and additional queries in random-self-reductions
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∘ There exist sets that are adaptively random-self-reducible but not nonadaptively random-self-reducible. Under plausible assumptions, there exist such sets inNP.
∘ There exists a function that has a nonadaptive (k(n)+1)-random-self-reduction but does not have an adaptivek(n)-random-self-reduction.
∘ Forany countable class of functionsC andany unbounded functionk(n), there exists a function that is nonadaptivelyk(n)-uniformly-random-self-reducible but is not inC/poly. This should be contrasted with Feigenbaum, Kannan, and Nisan's theorem that all nonadaptively 2-uniformly-random-self-reducible sets are inNP/poly.
Key wordsAdaptiveness random-self-reducibility
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