LFD Book Forum - View Single Post - slide #4 lecture 6 'Recursive Bound on B(N,k)'

yaser · #3 04-21-2013, 11:48 AM

Quote:

Originally Posted by skwong

1) The total is 14 (which matches with what was found in previous lecture),
but does not match with the B(N, k) calculation result of 15.

2) According to the numerical table in slide 8/18, the beta is 7, alpha
should be 1. I try to list them out like the above, but cannot know
which 7 combination to pick for beta rows, because I think I need to
kick out the 1010 and 0101 pattern. But then the 2 sections of beta
in the table will not be same for the x1 to x3.

1) The total is indeed 14 for the matrix you constructed, and for the perceprton case. The maximum possible is 15, though (take all posible patterns of 4 bits except the all 0's, and you have a break point of 4). Since

is an upper bound, there is no problem here.

2) In the matrix that excludes the all 0's, the set

contains only the pattern 0001, so $\alpha=1$ , while the set

contains the remaining 14 patterns (excluding all 0's) so $\beta=7$ .