## Abstract

Impagliazzo and Wigderson proved a uniform hardness vs. randomness "gap result" for BPP. We show an analogous result for AM: Either Arthur-Merlin protocols are very strong and everything in E = DTIME(2 ^{O(n)}) can be proved to a sub-exponential time verifier, or else Arthur-Merlin protocols are weak and every language in AM has a polynomial time nondeterministic algorithm in the uniform average-case setting (i.e., it is infeasible to come up with inputs on which the algorithm fails). For the class AM ⊂ coAM we can remove the average-case clause and show under the same assumption that AM ⊂ coAM = NP ⊂ coNP. A new ingredient in our proof is identifying a novel resiliency property of hardness vs. randomness trade-offs. We observe that the Miltersen-Vinodchandran generator has this property.

Original language | English |
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Pages (from-to) | 33-47 |

Number of pages | 15 |

Journal | Proceedings of the Annual IEEE Conference on Computational Complexity |

State | Published - 2003 |

Externally published | Yes |

Event | 18th Annual IEEE Conference on Computational Complexity - Aarhus, Denmark Duration: 7 Jul 2003 → 10 Jul 2003 |

## ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Computational Mathematics