Weak Derandomization of Weak Algorithms: Explicit Versions of Yao??s Lemma |
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Authors: | Ronen Shaltiel |
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Affiliation: | (1) Dept. Computer Science, University of Texas at Austin, 1 University Station C0500, Taylor Hall, 78712-1188 Austin, TX Texas, USA |
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Abstract: | A simple averaging argument shows that given a randomized algorithm A and a function f such that for every input x, PrA(x) = f(x)] ≥ 1 − ρ (where the probability is over the coin tosses of A), there exists a non-uniform deterministic algorithm B “of roughly the same complexity” such that PrB(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. |
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