# Testing Low-Degree Polynomials over GF(2)

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## Testing Low-Degree Polynomials over GF(2)

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### Presentations text content in Testing Low-Degree Polynomials over GF(2)

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Testing Low-Degree Polynomials over GF(2)

Noga

Alon

Simon Litsyn

Michael Krivelevich

Tali Kaufman

Dana Ron

Danny

Vainstein

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Definitions

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Definitions

Let

P

k

be all polynomials over {0,1}

n

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

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Definitions

Let

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

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Definitions

Let

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

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Definitions

Let

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

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Definitions

For any two functions :

The

symmetric difference is:

The

relative distance

is:

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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 ,

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Definitions

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Definitions

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Definitions

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Definitions

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Definitions

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Definitions

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Definitions

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Definitions

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Characterization Theorem

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Characterization Theorem

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Characterization Theorem

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Characterization Theorem- Reminder

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The Algorithm

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The Algorithm

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The Algorithm

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The Algorithm – cont.

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The Algorithm – cont.

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The Algorithm – cont.

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Definitions

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Definitions

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Definitions

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Lemmas

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Lemmas

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Lemmas

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Proof of Correctness

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Proof of Correctness

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Proof of Correctness

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Proof of Correctness

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Proof of Correctness

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Proof of Correctness

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Proof of Correctness

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Proof of Correctness

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Proof of Correctness

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Proof of Correctness

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Proof of Correctness

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Proof of Correctness

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Questions?

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