Error Reduction by Parallel Repetition—A Negative Result

We show that no fixed number of parallel repetitions suffices in order to reduce the error in two-prover one-round proof systems from one constant to another. Our results imply that the recent bounds proven by Ran Raz, showing that the number of rounds that suffice is inversely proportional to the answer length, are nearly best possible.

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Correspondence to Uriel Feige*.

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* Incumbent of the Joseph and Celia Reskin Career Development Chair.

† Supported in part by grant No. MQT 300 from the International Science Foundation and by an AMS-FSU grant.

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Feige*, U., Verbitsky†, O. Error Reduction by Parallel Repetition—A Negative Result. Combinatorica 22, 461–478 (2002).

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  • Proof System
  • Error Reduction
  • Parallel Repetition
  • Recent Bound
  • Answer Length