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

2. Definitions

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

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

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

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

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

8. 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,

9. Definitions

17. Characterization Theorem

47. Characterization Theorem- Reminder

48. The Algorithm

51. The Algorithm – cont.

54. Definitions

57. Lemmas

60. Proof of Correctness

72. Questions?