On Yao's XOR-Lemma

@article{Goldreich1995OnYX,
  title={On Yao's XOR-Lemma},
  author={Oded Goldreich and Noam Nisan and Avi Wigderson},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={1995},
  volume={2}
}
A fundamental lemma of Yao states that computational weakunpredictability of Boolean predicates is amplified when 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 concatenating the values of the original function on several independent instances is much more unpredictable, with respect to specified complexity bounds, than the… CONTINUE READING
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References

Publications referenced by this paper.
SHOWING 1-7 OF 7 REFERENCES

Hard-core distributions for somewhat hard problems

  • Proceedings of IEEE 36th Annual Foundations of Computer Science
  • 1995
VIEW 3 EXCERPTS

Products and help bits in decision trees

  • Proceedings 35th Annual Symposium on Foundations of Computer Science
  • 1994
VIEW 1 EXCERPT

Hardness vs. randomness

  • [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
  • 1988
VIEW 1 EXCERPT