You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
44 lines
1.2 KiB
44 lines
1.2 KiB
// Knuth's model of a fair die using only fair coins
|
|
dtmc
|
|
|
|
const double p;
|
|
const double q;
|
|
|
|
module die1
|
|
|
|
// local state
|
|
s1 : [0..7] init 0;
|
|
// value of the dice
|
|
d1 : [0..6] init 0;
|
|
|
|
[] s1=0 -> p : (s1'=1) + 1-p : (s1'=2);
|
|
[] s1=1 -> q : (s1'=3) + 1-q : (s1'=4);
|
|
[] s1=2 -> q : (s1'=5) + 1-q : (s1'=6);
|
|
[] s1=3 -> p : (s1'=1) + 1-p : (s1'=7) & (d1'=1);
|
|
[] s1=4 -> p : (s1'=7) & (d1'=3) + 1-p : (s1'=7) & (d1'=2);
|
|
[] s1=5 -> p : (s1'=2) + 1-p : (s1'=7) & (d1'=4);
|
|
[] s1=6 -> p : (s1'=7) & (d1'=6) + 1-p : (s1'=7) & (d1'=5);
|
|
[] s1=7 -> 1: (s1'=7);
|
|
|
|
endmodule
|
|
|
|
module die2 = die1 [ s1=s2, s2=s1, d1=d2 ] endmodule
|
|
|
|
rewards "coin_flips"
|
|
[] s1<7 | s2<7 : 1;
|
|
endrewards
|
|
|
|
label "two" = s1=7 & s2=7 & d1+d2=2;
|
|
label "three" = s1=7 & s2=7 & d1+d2=3;
|
|
label "four" = s1=7 & s2=7 & d1+d2=4;
|
|
label "five" = s1=7 & s2=7 & d1+d2=5;
|
|
label "six" = s1=7 & s2=7 & d1+d2=6;
|
|
label "seven" = s1=7 & s2=7 & d1+d2=7;
|
|
label "eight" = s1=7 & s2=7 & d1+d2=8;
|
|
label "nine" = s1=7 & s2=7 & d1+d2=9;
|
|
label "ten" = s1=7 & s2=7 & d1+d2=10;
|
|
label "eleven" = s1=7 & s2=7 & d1+d2=11;
|
|
label "twelve" = s1=7 & s2=7 & d1+d2=12;
|
|
label "same" = s1=7 & s2=7 & d1=d2;
|
|
|
|
label "end" = s1=7 & s2=7;
|