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45 lines
1.4 KiB
45 lines
1.4 KiB
// Knuth's model of a fair die using only fair coins
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mdp
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module die
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// local state
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s : [0..7] init 0;
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// value of the dice
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d : [0..6] init 0;
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[fair] s=0 -> 0.5 : (s'=1) + 0.5 : (s'=2);
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[ufair1] s=0 -> 0.6 : (s'=1) + 0.4 : (s'=2);
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[ufair2] s=0 -> 0.7 : (s'=1) + 0.3 : (s'=2);
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[fair] s=1 -> 0.5 : (s'=3) + 0.5 : (s'=4);
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[ufair1] s=1 -> 0.6 : (s'=3) + 0.4 : (s'=4);
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[ufair2] s=1 -> 0.7 : (s'=3) + 0.3 : (s'=4);
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[fair] s=2 -> 0.5 : (s'=5) + 0.5 : (s'=6);
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[ufair1] s=2 -> 0.6 : (s'=5) + 0.4 : (s'=6);
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[ufair2] s=2 -> 0.7 : (s'=5) + 0.3 : (s'=6);
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[fair] s=3 -> 0.5 : (s'=1) + 0.5 : (s'=7) & (d'=1);
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[ufair1] s=3 -> 0.6 : (s'=1) + 0.4 : (s'=7) & (d'=1);
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[ufair2] s=3 -> 0.7 : (s'=1) + 0.3 : (s'=7) & (d'=1);
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[fair] s=4 -> 0.5 : (s'=7) & (d'=2) + 0.5 : (s'=7) & (d'=3);
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[ufair1] s=4 -> 0.6 : (s'=7) & (d'=2) + 0.4 : (s'=7) & (d'=3);
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[ufair2] s=4 -> 0.7 : (s'=7) & (d'=2) + 0.3 : (s'=7) & (d'=3);
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[fair] s=5 -> 0.5 : (s'=7) & (d'=4) + 0.5 : (s'=7) & (d'=5);
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[ufair1] s=5 -> 0.6 : (s'=2) + 0.4 : (s'=7) & (d'=6);
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[ufair2] s=5 -> 0.7 : (s'=2) + 0.3 : (s'=7) & (d'=6);
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[] s=7 -> 1: (s'=7);
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endmodule
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rewards "coin_flips"
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[fair] s<7 : 1;
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[ufair1] s<7 : 1;
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[ufair2] s<7 : 1;
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endrewards
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label "one" = s=7&d=1;
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label "two" = s=7&d=2;
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label "three" = s=7&d=3;
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label "four" = s=7&d=4;
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label "five" = s=7&d=5;
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label "six" = s=7&d=6;
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label "done" = s=7;
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