On Nonadaptive Reductions to the Set of Random Strings and Its Dense Subsets

Vaughan Jones, Kolmogorov Complexity, and the New Complexity Landscape around Circuit Minimization

“…These results attracted considerable attention, because prior work had indicated that such worst-case-to-average-case reductions would be impossible to prove using black-box techniques. Additional work has given further evidence that the techniques of [27] are inherently non-black-box [32].…”

“…I won't repeat that discussion here, because both of those conjectures have been disproved (barring some extremely unlikely complexity class collapses). Taken together, the papers [32], [29], and [28] give a much better understanding of the classes of languages reducible to the Kolmogorov-random strings.…”

The New Complexity Landscape Around Circuit Minimization

“…These results attracted considerable attention, because prior work had indicated that such worst-case-to-average-case reductions would be impossible to prove using black-box techniques. Additional work has given further evidence that the techniques of [19] are inherently nonblack-box [24].…”

“…I won't repeat that discussion here, because both of those conjectures have been disproved (barring some extremely unlikely complexity class collapses). Taken together, the papers [21,24], and [20] give a much better understanding of the classes of languages reducible to the Kolmogorov-random strings.…”