We show that if an NP-complete problem has a non-adaptive
self-corrector with respect to a samplable distribution then
coNP is contained in NP/poly and the polynomial
hierarchy collapses to the third level. Feigenbaum and
Fortnow (SICOMP 22:994-1005, 1993) show the same conclusion
under the stronger assumption that an
NP-complete problem has a non-adaptive random self-reduction.

Our result shows that the average-case hardness of a problem in
NP or the security of a one-way function cannot be
based (using non-adaptive reductions) on the worst-case complexity
of an \np-complete problem (unless the polynomial hierarchy
collapses).