The power of adaptiveness and additional queries in random-self-reductions

Relationships between adaptive and nonadaptive random-self-reductions are examined. The question of what happens to random-self-reductions if the number of queries they are allowed to make is restricted is also explored. The following results are shown. (1) There exist sets that are adaptively random-self-reducible but not nonadaptively random-self-reducible. Under reasonable assumptions, there exist such sets in NP. (2) There exists a function that has a nonadaptive (k+1)-random-self-reduction but does not have an adaptive k-random-self-reduction. (3) For any countable class of functions C and any unbounded function k(n), there exists a function that is nonadaptively k-uniformly-random-self-reducible but is not in C/poly