Lower bounds on random-self-reducibility

The limitations of random-self-reducibility are studied, and several negative results are proved. For example, it is shown unconditionally that random Boolean functions do not have random self-reductions, even of a quite general nature. For several natural, but less general, classes of random self-reductions, it is shown that, unless the polynomial hierarchy collapses, nondeterministic polynomial-time computable functions are not random-self-reducible