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
Slide20Slide21Slide22Slide23Slide24Slide25Slide26Slide27Slide28Slide29Slide30Slide31Slide32Slide33Slide34Slide35Slide36Slide37Slide38Slide39Slide40Slide41Slide42Slide43Slide44Slide45Slide46Slide47Characterization 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?
Slide73Slide74Slide75Slide76
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