Revision #2 Authors: Oded Goldreich, Noam Nisan, Avi Wigderson

Accepted on: 3rd July 2010 09:09

Downloads: 2164

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Since the first publication of this survey, Yao's XOR Lemma has been the subject of intensive research. The current revision contains a short review of this research (see Section 7), but the main text (i.e., Sections 1-6) is not updated according to these subsequent discoveries. The current version also include a new appendix (Appendix B), which discusses a variant of the XOR Lemma, called the Selective XOR Lemma.

Revision #1 Authors: Oded Goldreich, Noam Nisan, Avi Wigderson

Accepted on: 14th January 1999 00:00

Downloads: 1823

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A fundamental Lemma of Yao states that computational

weak-unpredictability

of functions gets amplified if the results of several independent

instances are XOR together.

We survey two known proofs of Yao's Lemma and present

a third alternative proof.

The third proof proceeds by first proving that a function constructed

by {\em concatenating} the values of the function

on several independent instances is much more unpredictable,

with respect to specified complexity bounds,

than the original function.

This statement turns out to be easier to prove than the XOR-Lemma.

Using a result of Goldreich and Levin

and some elementary observation, we derive the XOR-Lemma.

TR95-050 Authors: Oded Goldreich, Noam Nisan, Avi Wigderson

Publication: 20th October 1995 08:17

Downloads: 1265

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Comment #1 Authors: Oded Goldreich, Noam Nisan, Avi Wigderson

Accepted on: 8th December 1995 09:03

Downloads: 1468

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We correct some typos in the proof of Lemma 12.

Specifically, the probability bound in Claim 12.3

should be $(1/2)+2\epsilon$ (rather than $(1/2)+(\epsilon/2)$)

and the last line in the bound on the expectation

of $\sum_{x\in C}\zeta_xw_x$

should be $\rho(n)\cdot[(1/2)+\epsilon]$

(rather than $\rho(n)\cdot[(1/2)-\epsilon]$).