General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

Example 298
# A B C D V
0 F F F F F
1 F F F T F
2 F F T F F
3 F F T T F
4 F T F F F
5 F T F T F
6 F T T F T
7 F T T T F
8 T F F F T
9 T F F T T
10 T F T F T
11 T F T T T
12 T T F F T
13 T T F T T
14 T T T F T
15 T T T T F
The corresponding KV-map:
AB AB AB AB
CD F F T T
CD F F T T
CD F F F T
CD F T T T
in the red/brown group
A does not change, so include A
B changes, so do not include it
C does not change, so include C
D changes, so do not include it
So the monomial is A C
in the green/brown group we have A B
in the blue group we have B C D
The minimal polynomial for E(6, 8, 9, 10, 11, 12, 13, 14) is A B + A C + B C D
KV-maps Caveats
c○: Michael Kohlhase 171
groups are always rectangular of size 2 k (no crooked shapes!)
a group of size 2 k induces a monomial of size n − k (the bigger the better)
groups can straddle vertical borders for three variables
groups can straddle horizontal and vertical borders for four variables
picture the the n-variable case as a n-dimensional hypercube!
c○: Michael Kohlhase 172
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