Random polynomial time is equal to slightly-random polynomial time

Abstract

Random Polynomial Time (Rp) is currently considered to be the class of tractable computational problems. Here one assumes a source of truly random bits. However, the known sources of randomness are imperfect. They can be modeled as an adversary source, called slightly-random source. Slightlyrandom Polynomial Time (SRp) is the class of problems solvable in polynomial time using such a source. SRp is thus a more realistic definition of a tractable computational problem. In this paper we give an affirmative answer to the question "is Rp = SRp?" Our proof method is constructive: given an Rp algorithm for a problem, we show how to obtain an SRp algorithm for it. Studying the relationship between randomized and deterministic computation is currently an important issue. A central question here is "is Rp = P?" Our result may be a step towards answering this question.