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40 lines
1.2 KiB
40 lines
1.2 KiB
// sum of two dice as the asynchronous parallel composition of
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// two copies of Knuth's model of a fair die using only fair coins
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mdp
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module die1
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// local state
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s1 : [0..7] init 0;
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// value of the dice
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d1 : [0..6] init 0;
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[] s1=0 -> 0.5 : (s1'=1) + 0.5 : (s1'=2);
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[] s1=1 -> 0.5 : (s1'=3) + 0.5 : (s1'=4);
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[] s1=2 -> 0.5 : (s1'=5) + 0.5 : (s1'=6);
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[] s1=3 -> 0.5 : (s1'=1) + 0.5 : (s1'=7) & (d1'=1);
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[] s1=4 -> 0.5 : (s1'=7) & (d1'=2) + 0.5 : (s1'=7) & (d1'=3);
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[] s1=5 -> 0.5 : (s1'=7) & (d1'=4) + 0.5 : (s1'=7) & (d1'=5);
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[] s1=6 -> 0.5 : (s1'=2) + 0.5 : (s1'=7) & (d1'=6);
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[] s1=7 & s2=7 -> 1: (s1'=7);
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endmodule
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module die2 = die1 [ s1=s2, s2=s1, d1=d2 ] endmodule
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rewards "coinflips"
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[] s1<7 | s2<7 : 1;
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endrewards
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label "done" = s1=7 & s2=7;
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label "two" = s1=7 & s2=7 & d1+d2=2;
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label "three" = s1=7 & s2=7 & d1+d2=3;
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label "four" = s1=7 & s2=7 & d1+d2=4;
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label "five" = s1=7 & s2=7 & d1+d2=5;
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label "six" = s1=7 & s2=7 & d1+d2=6;
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label "seven" = s1=7 & s2=7 & d1+d2=7;
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label "eight" = s1=7 & s2=7 & d1+d2=8;
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label "nine" = s1=7 & s2=7 & d1+d2=9;
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label "ten" = s1=7 & s2=7 & d1+d2=10;
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label "eleven" = s1=7 & s2=7 & d1+d2=11;
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label "twelve" = s1=7 & s2=7 & d1+d2=12;
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