Lower Bounds for Testing Properties of Functions on Hypergrids Grigory Yaroslavtsev Joint with: Eric Blais (MIT) Sofya Raskhodnikova.

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Presentation transcript:

Lower Bounds for Testing Properties of Functions on Hypergrids Grigory Yaroslavtsev Joint with: Eric Blais (MIT) Sofya Raskhodnikova (PSU)

Property Testing [Goldreich, Goldwasser, Ron, Rubinfeld, Sudan] No YES Randomized algorithm YES No Property tester Don’t care

Ultra-fast Approximate Decision Making

Property Testing [Goldreich, Goldwasser, Ron, Rubinfeld, Sudan]

Communication Complexity [Yao’79] Shared randomness …

{

Property testing lower bounds via CC Monotonicity, Juntas, Low Fourier degree, Small Decision Trees [Blais, Brody, Matulef’11] Small-width OBDD properties [Brody, Matulef, Wu’11] Lipschitz property [Jha, Raskhodnikova’11] Codes [Goldreich’13, Gur, Rothblum’13] Number of relevant variables [Ron, Tsur’13] (Almost) all: Boolean functions over Boolean hypercube

…

Open Problems