Lower bounds on random-self-reducibility

J. Feigenbaum, S. Kannan, N. Nisan
Proceedings Fifth Annual Structure in Complexity Theory Conference  
Informally speaking, a function f is random-self-reducible if, for any x, the computation of f(x) can be reduced to the computation of f on other \randomly chosen" inputs. Such functions are fundamental in many areas of theoretical computer science, including lower bounds, pseudorandom number-generators, interactive proof systems, zeroknowledge, instance-hiding, program-checking, and program-testing. Several examples of random-selfreductions are quite well-known and have been applied in all of
more » ... hese areas. In this paper we study the limitations of randomself-reducibility and prove several negative results. For example, we show unconditionally that random boolean functions do not have random-selfreductions, even of a quite general nature. For several natural, but less general, classes of random-selfreductions, we show that, unless the polynomial hierarchy collapses, nondeterminstic polynomial-time computable functions are not random-self-reducible.
doi:10.1109/sct.1990.113959 dblp:conf/coco/FeigenbaumKN90 fatcat:vwerkcayyvec5g5npfebebkg2a