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# Testing Low-Degree Polynomials over GF(2) PowerPoint Presentation, PPT - DocSlides

trish-goza | 2016-11-13 | General
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Noga. . Alon. Simon . Litsyn. Michael . Krivelevich. Tali. Kaufman. Dana Ron. Danny . Vainstein. Definitions. Definitions. Let. . P. k. . be all polynomials over {0,1}. n. with degree at most k without a free term (over GF(2)).. ID: 488169

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Testing Low-Degree Polynomials over GF(2)

Noga

Alon

Simon Litsyn

Michael Krivelevich

Tali Kaufman

Dana Ron

Danny

Vainstein

Slide2Definitions

Slide3Definitions

Let

P

k

be all polynomials over {0,1}

n

with degree at most k without a free term (over GF(2)).

Slide4Definitions

Let

Pk be all polynomials over {0,1}n with degree at most k without a free term (over GF(2)).

Slide5Definitions

Let

Pk be all polynomials over {0,1}n with degree at most k without a free term (over GF(2)).

Slide6Definitions

Let

Pk be all polynomials over {0,1}n with degree at most k without a free term (over GF(2)).

Slide7Definitions

For any two functions :

The

symmetric difference is:

The

relative distance

is:

Slide8Definitions

For any two functions :

The

symmetric difference is:

The

relative distance

is:

For a function

f

and a family of functions G, we say that f is -far from G, for some if for every ,

Slide9Definitions

Slide10Definitions

Slide11Definitions

Slide12Definitions

Slide13Definitions

Slide14Definitions

Slide15Definitions

Slide16Definitions

Slide17Characterization Theorem

Slide18Characterization Theorem

Slide19Characterization Theorem

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Characterization Theorem- Reminder

Slide48The Algorithm

Slide49The Algorithm

Slide50The Algorithm

Slide51The Algorithm – cont.

Slide52The Algorithm – cont.

Slide53The Algorithm – cont.

Slide54Definitions

Slide55Definitions

Slide56Definitions

Slide57Lemmas

Slide58Lemmas

Slide59Lemmas

Slide60Proof of Correctness

Slide61Proof of Correctness

Slide62Proof of Correctness

Slide63Proof of Correctness

Slide64Proof of Correctness

Slide65Proof of Correctness

Slide66Proof of Correctness

Slide67Proof of Correctness

Slide68Proof of Correctness

Slide69Proof of Correctness

Slide70Proof of Correctness

Slide71Proof of Correctness

Slide72Questions?

Slide73Slide74

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