From 489fd4f780db1deba3ed453f2800fe69d4f0e5a8 Mon Sep 17 00:00:00 2001
From: sjunges <sebastian.junges@rwth-aachen.de>
Date: Thu, 20 Oct 2016 01:42:00 +0200
Subject: [PATCH] Die and TwoDie as in the Qapl talk

Former-commit-id: 93f21ffea34b8fff4fae4ae6a41c2bb8f67b0ae1 [formerly 88343ceb7b65aeb964dbccc0765eae51faadc683]
Former-commit-id: 1595b7eaac1932190e96f023350f97254cc52099
---
 examples/pdtmc/die.pm    | 35 ++++++++++++++++++++++++++++++++
 examples/pdtmc/twodie.pm | 44 ++++++++++++++++++++++++++++++++++++++++
 2 files changed, 79 insertions(+)
 create mode 100644 examples/pdtmc/die.pm
 create mode 100644 examples/pdtmc/twodie.pm

diff --git a/examples/pdtmc/die.pm b/examples/pdtmc/die.pm
new file mode 100644
index 000000000..31290bd69
--- /dev/null
+++ b/examples/pdtmc/die.pm
@@ -0,0 +1,35 @@
+// 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;
diff --git a/examples/pdtmc/twodie.pm b/examples/pdtmc/twodie.pm
new file mode 100644
index 000000000..d38f75496
--- /dev/null
+++ b/examples/pdtmc/twodie.pm
@@ -0,0 +1,44 @@
+// 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;