A parallel repetition theorem for any interactive argument

Iftach Haitner*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The question of whether or not parallel repetition reduces the soundness error is a fundamental question in the theory of protocols. While parallel repetition reduces (at an exponential rate) the error in interactive proofs and (at a weak exponential rate) in special cases of interactive arguments (e.g., 3-message protocols - Bellare, Impagliazzo and Naor [FOCS '97], and public-coin protocols - Håstad, Pass, Pietrzak and Wikström [Manuscript '08]), Bellare et al. gave an example of interactive arguments for which parallel repetition does not reduce the soundness error at all. We show that by slightly modifying any interactive argument, in a way that preserves its completeness and only slightly deteriorates its soundness, we get a protocol for which parallel repetition does reduce the error at a weak exponential rate. In this modified version, the verifier flips at the beginning of each round an (1 - 1/4m, 1/4m) biased coin (i.e., 1 is tossed with probability 1/4m), where m is the round complexity of the (original) protocol. If the coin is one, the verifier halts the interaction and accepts, otherwise it sends the same message that the original verifier would. At the end of the protocol (if reached), the verifier accepts if and only if the original verifier would.

Original languageEnglish
Title of host publicationProceedings - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009
Number of pages10
StatePublished - 2009
Externally publishedYes
Event50th Annual Symposium on Foundations of Computer Science, FOCS 2009 - Atlanta, GA, United States
Duration: 25 Oct 200927 Oct 2009

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428


Conference50th Annual Symposium on Foundations of Computer Science, FOCS 2009
Country/TerritoryUnited States
CityAtlanta, GA


  • Computationally sound proofs
  • Hardness amplification
  • Interactive arguments
  • Parallel repetition

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