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A parallel repetition theorem for any interactive argument (2009).
| Content Provider | CiteSeerX |
|---|---|
| Author | Haitner, Iftach |
| Description | This content is published in 50th Annual IEEE Symposium On Foundations Of Computer Science |
| Abstract | 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 — H˚astad, 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 1 4m 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. |
| File Format | |
| Publisher Date | 2009-01-01 |
| Access Restriction | Open |
| Subject Keyword | Interactive Argument Parallel Repetition Computer Science Parallel Repetition Theorem 50th Annual Ieee Symposium Weak Exponential Rate Original Verifier Soundness Error Sound Proof Wikstr Manuscript Keywords-hardness Amplification Interactive Proof Naor Focs Exponential Rate Public-coin Protocol Astad Fundamental Question Verifier Flip 3-message Protocol Bellare Round Complexity Special Case Parallel Repetition Reduces Modified Version |
| Content Type | Text |
| Resource Type | Conference Proceedings |
