Die and TwoDie as in the Qapl talk

Former-commit-id: 93f21ffea3 [formerly 88343ceb7b]
Former-commit-id: 1595b7eaac

examples/pdtmc/die.pm

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+// Knuth's model of a fair die using only fair coins
+dtmc
+
+const double p;
+const double q;
+
+module die
+
+	// local state
+	s : [0..7] init 0;
+	// value of the dice
+	d : [0..6] init 0;
+	
+	[] s=0 -> p : (s'=1) + 1-p : (s'=2);
+	[] s=1 -> q : (s'=3) + 1-q : (s'=4);
+	[] s=2 -> q : (s'=5) + 1-q : (s'=6);
+	[] s=3 -> p : (s'=1) + 1-p : (s'=7) & (d'=1);
+	[] s=4 -> p : (s'=7) & (d'=3) + 1-p : (s'=7) & (d'=2);
+	[] s=5 -> p : (s'=2) + 1-p : (s'=7) & (d'=6);
+	[] s=6 -> p : (s'=7) & (d'=6) + 1-p : (s'=7) & (d'=5);
+	[] s=7 -> 1: (s'=7);
+	
+endmodule
+
+rewards "coin_flips"
+	[] s<7 : 1;
+endrewards
+
+label "one" = s=7&d=1;
+label "two" = s=7&d=2;
+label "three" = s=7&d=3;
+label "four" = s=7&d=4;
+label "five" = s=7&d=5;
+label "six" = s=7&d=6;
+label "end" = s=7;

examples/pdtmc/twodie.pm

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+// 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;