add lab3 exercises

lab3/exercise/ex1.2/lake2.pha

@@ -0,0 +1,47 @@
+r_in_r := 30;
+r_in_d := 10;
+r_out := 15.7;
+
+automaton lake
+contr_var: x, t, c;
+
+synclabs: lakelab;
+loc dry: 
+    while x >= 0 & c <= 0.75 wait 
+        { 0.7 * r_in_d - r_out <= x' <= r_in_d - r_out & t' == 1 & c' == 1}
+    when (c >= 0.75) sync lakelab goto rain;
+    
+loc rain:
+    while x >= 0 & c <= 1 wait 
+        { 0.7 * r_in_r - r_out <= x' <= r_in_r - r_out & t' == 1 & c' == 1}
+    when (c >= 1) sync lakelab do {c' == 0 & t' == t & x' == x} goto dry;
+    
+initially: dry & x == 25.7 & t == 0 & c == 0;
+end
+
+
+
+// Compute the reachable set
+//
+region=lake.reachable;
+
+//
+// Output to file
+
+region.print("lake2_regions.txt", 0);
+
+region.project_to(t, x);
+region.print("lake2.txt", 2);
+
+// Safety verification
+
+forbidden = lake.{$ & x < 0};
+reach_set = lake.is_reachable(forbidden);
+reach_set.intersection_assign(forbidden);
+
+echo "The intersection between the reachable set and the bad region is:";
+reach_set.is_empty;
+
+
+
+