Abstract
We study random-self-reductions from a structural complexity-theoretic point of view. Specifically, we look at relationships between adaptive and nonadaptive random-self-reductions. We also look at what happens to random-self-reductions if we restrict the number of queries they are allowed to make. We show the following results:
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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.
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∘ There exists a function that has a nonadaptive (k(n)+1)-random-self-reduction but does not have an adaptivek(n)-random-self-reduction.
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∘ 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.
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Feigenbaum, J., Fortnow, L., Lund, C. et al. The power of adaptiveness and additional queries in random-self-reductions. Comput Complexity 4, 158–174 (1994). https://doi.org/10.1007/BF01202287
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DOI: https://doi.org/10.1007/BF01202287