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Property Testing and Communication Complexity Grigory Yaroslavtsev http://grigory.us
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Property Testing [Goldreich, Goldwasser, Ron, Rubinfeld, Sudan] No YES Randomized algorithm YES No Property tester Don’t care
![Property Testing [Goldreich, Goldwasser, Ron, Rubinfeld, Sudan] No YES Randomized algorithm YES No Property tester Don’t care](http://images.slideplayer.com./8/2453247/slides/slide_2.jpg "Property Testing [Goldreich, Goldwasser, Ron, Rubinfeld, Sudan] No YES Randomized algorithm YES No Property tester Don’t care")
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Property Testing [Goldreich, Goldwasser, Ron, Rubinfeld, Sudan]
![Property Testing [Goldreich, Goldwasser, Ron, Rubinfeld, Sudan]](http://images.slideplayer.com./8/2453247/slides/slide_3.jpg "Property Testing [Goldreich, Goldwasser, Ron, Rubinfeld, Sudan]")
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Communication Complexity [Yao’79] Shared randomness …
![Communication Complexity [Yao’79] Shared randomness …](http://images.slideplayer.com./8/2453247/slides/slide_4.jpg "Communication Complexity [Yao’79] Shared randomness …")
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Communication Direct Sums
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Specialized Communication Direct Sums
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Direct Sums in Property Testing [Woodruff, Y.]
![Direct Sums in Property Testing [Woodruff, Y.]](http://images.slideplayer.com./8/2453247/slides/slide_10.jpg "Direct Sums in Property Testing [Woodruff, Y.]")
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Property Testing Direct Sums [Goldreich’13]
![Property Testing Direct Sums [Goldreich’13]](http://images.slideplayer.com./8/2453247/slides/slide_12.jpg "Property Testing Direct Sums [Goldreich’13]")
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[Goldreich ‘13]
![[Goldreich ‘13]](http://images.slideplayer.com./8/2453247/slides/slide_13.jpg "[Goldreich ‘13]")
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Reduction from Simultaneous Communication [Woodruff]
![Reduction from Simultaneous Communication [Woodruff]](http://images.slideplayer.com./8/2453247/slides/slide_14.jpg "Reduction from Simultaneous Communication [Woodruff]")
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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] All functions are over Boolean hypercube
![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] All functions are over Boolean hypercube](http://images.slideplayer.com./8/2453247/slides/slide_15.jpg "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] All functions are over Boolean hypercube")
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Thank you!
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