Testing Low-Degree Polynomials over GF(2) Noga AlonSimon LitsynMichael Krivelevich Tali KaufmanDana Ron Danny Vainstein.

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Presentation transcript:

Testing Low-Degree Polynomials over GF(2) Noga AlonSimon LitsynMichael Krivelevich Tali KaufmanDana Ron Danny Vainstein

Definitions

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

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

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

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

Definitions For any two functions : The symmetric difference is: The relative distance is:

Definitions 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,

Definitions

Characterization Theorem

Characterization Theorem- Reminder

The Algorithm

The Algorithm – cont.

Definitions

Lemmas

Proof of Correctness

Questions?