SELF-CHECK ALGORITHM(F): |
ALGORITHM SELF-CHECK-DIAG(F): |
LEMMA: If F is a diagonal linear function, then SELF-CHECK(F) (above) passes. If F is not an approximately diagonal linear function, then SELF-CHECK(F) fails with probability at least 50%. |
LEMMA: If F is a diagonal linear function, then SELF-CHECK-DIAG(F) (above) passes. If F is not an approximately diagonal linear function, then SELF-CHECK-DIAG(F) fails with probability at least 50%. |
If F is diagonal linear, then SELF-CHECK clearly passes. |
If F is diagonal linear, then SELF-CHECK-DIAG clearly passes. |
Thus, if G is not diagonal linear, then each of the last three checks made by the SELF-CHECK algorithm |
Thus, if G is not diagonal linear, then each of the last three checks made by the SELF-CHECK-DIAG algorithm |
Thus, if G is not diagonal linear, then the SELF-CHECK will fail with probability at least 1-(1-7/40)3 > 1/2. |
Thus, if G is not diagonal linear, then the SELF-CHECK-DIAG will fail with probability at least 1-(1-7/40)3 > 1/2. |
* M. Blum, M. Luby, and R. Rubinfeld. Self-testing/correcting with applications to numerical problems. In Proc. 22nd ACM Symp. on Theory of Computing, pages 73-83, 1990. |
* M. Blum, M. Luby, and R. Rubinfeld. Self-testing/correcting with applications to numerical problems. In Proc. 22nd ACM Symp. on Theory of Computing, pages 73-83, 1990. |