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Boolean Games
- 14. Task: construct a set of Horn clauses that
describe if a player has already won
or lost.
- 31. x1 x3 x5 x7
x6x4 x8
x9
1
some example steps
- max 4 possible moves
-
start
- 32. x1 x3 x5 x7
x6 x8
x9
1 0
some example steps
- max 4 possible moves
-
start
- 33. x1 x5 x7
x6 x8
x9
1 0
1
some example steps
- max 4 possible moves
-
start
- 34. x1 x5 x7
x6 x8
x9
0
1
0
some example steps
- max 4 possible moves
-
start
- 43. n (a)
2 0 wins
3 0 wins
4 first wins
5 second wins
6 second wins
7 1 loses if first
8 draw
9 draw
(a) f(x[1:n]) = x[1:n] < x[n:1]╓
╙
╓
╙
- 44. n (b)
2 second wins
3 first wins
4 first wins
5 draw
6 second wins
7 second wins
8 draw
9 draw
(b) f(x[1:n]) = xi⊕i
- 45. n (c)
2 1 wins
3 first wins
4 first wins
5 draw
6 1 loses if first
7 1 loses if first
8 draw
9 draw
(c) f(x[1:n]) = x[1:n] contains
no two consecutive 1’s
╓
╙ ╓
╙
- 46. n (d)
2 second wins
3 first wins
4 first wins
5 1 loses if first
6 1 loses if first
7 1 loses if first
8 1 loses if first
9 1 loses if first
(d) f(x[1:n]) = (x[1:n])2 is prime╓
╙
╓
╙