Two Sides of the Coin Problem Gil Cohen Joint with: Anat Ganor and Ran Raz.

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Presentation transcript:

Two Sides of the Coin Problem Gil Cohen Joint with: Anat Ganor and Ran Raz

The Coin Problem

Promise Majority [Ajtai83, AjtaiBenOr84, Stockmeyer85, Ajtai93, Amano09, Viola09, Viola11, KoppartySrinivasan12, CDIKMRR13]

The Coin Problem Promise Majority [O’DonnellWimmer07, Amano09] Approximating Majority

The Coin Problem Promise Majority [ShaltielViola08, Aaronson10, BrodyVerbin10, Steinberger13] Approximating Majority The Coin Problem

Read Once Branching Programs Outperforms the naïve “take the last sample” algorithm.

It is All About the Bias Theorem 1 (informal). It is all about the bias - ROBPs cannot make use of the dependencies.

It is All About the Bias Proof Idea. Black-box reduction to the coin problem.

AC Circuits 0 Motivation came from hardness amplification and oracle separation between BQP and PH, respectively.

Random Restrictions Majority Or =

Distinguishability and Random Restrictions Definition. When.

Summary and Open Problems * For ROBPs it is all about the bias. Thank you for your attention! * Any application of the SV result for PRGs?