= Trace the Winnow algorithm with 3: 1 for the following input. Suppose the domain is vectors of length n = 6 over {V1, V2, V3, V4, V5, V6} and the actual labels are with respect to formula v₁/v3/v6; for example, the true label of (1, 0, 1, 0, 1, 1) is '1' and that of 1, 1, 1, 1, 1,0 is '0'. The input vectors are: x1 = (1, 0, 1, 1, 0, 1) x2 = (1,0,1,1,0,0) x3 = x4= X5 x6 x7 x8 = = = = x9 = (0, 1, 0, 1, 0, 1) 1, 1, 1, 0, 0, 1) (1, (0, 1, 1, 1, 1,0) (1, 1, 1, 1, 1, 1) (0, 1, 0, 1, 1, 1) (1, 1, 0, 1, 1, 1) (1, 0, 1, 0, 0, 1) You need to follow the same assumptions as in the example in Slide 4 of Module 11. Show your work and specify whether it is possible that the algorithm makes more mistakes after processing the above vectors; justify your answer.

= Trace the Winnow algorithm with 3: 1 for the following input. Suppose the domain is vectors of length n = 6 over {V1, V2, V3, V4, V5, V6} and the actual labels are with respect to formula v₁/v3/v6; for example, the true label of (1, 0, 1, 0, 1, 1) is '1' and that of 1, 1, 1, 1, 1,0 is '0'. The input vectors are: x1 = (1, 0, 1, 1, 0, 1) x2 = (1,0,1,1,0,0) x3 = x4= X5 x6 x7 x8 = = = = x9 = (0, 1, 0, 1, 0, 1) 1, 1, 1, 0, 0, 1) (1, (0, 1, 1, 1, 1,0) (1, 1, 1, 1, 1, 1) (0, 1, 0, 1, 1, 1) (1, 1, 0, 1, 1, 1) (1, 0, 1, 0, 0, 1) You need to follow the same assumptions as in the example in Slide 4 of Module 11. Show your work and specify whether it is possible that the algorithm makes more mistakes after processing the above vectors; justify your answer.