Weak Derandomization of Weak Algorithms: Explicit Versions of Yao's Lemma

—A simple averaging argument shows that given a randomized algorithm A and a function f such that for every input x, Pr[A(x) = f(x)] ≥ 1−ρ (where the probability is over the coin tosses of A), there exists a nonuniform deterministic algorithm B “of roughly the same complexity” such that Pr[B(x) = f(x)] ≥ 1 − ρ (where the probability is over a uniformly chosen input x). This implication is often referred to as “the easy direction of Yao’s lemma” and can be thought of as “weak derandomization” in the sense that B is deterministic but only succeeds on most inputs. The implication follows as there exists a fixed value r for the random coins of A such that “hardwiring r into A” produces a deterministic algorithm B. However, this argument does not give a way to explicitly construct B. In this paper we consider the task of proving uniform versions of the implication above. That is, how to explicitly construct a deterministic algorithm B when given a randomized a...

• Type: Conference
• Year: 2009
• Where: COCO
• Authors: Ronen Shaltiel
• Keywords: COCO 2009, Deterministic Algorithm, Nonuniform Deterministic Algorithm, Randomized Algorithms, Theoretical Computer Science