add lab3 exercises

lab3/exercise/ex1.1/lake.pha

@@ -0,0 +1,40 @@
+r_in := 15;
+r_out := 15.7;
+
+automaton lake
+contr_var: x, t;
+
+synclabs: lakelab;
+loc single: 
+    while x >= 0 wait 
+        { 0.7 * r_in - r_out <= x' <= r_in - r_out & t' == 1}
+    
+initially: single & x == 25.7 & t == 0;
+end
+
+
+
+// Compute the reachable set
+//
+region=lake.reachable;
+
+//
+// Output to file
+
+region.print("lake_regions.txt", 0);
+
+region.project_to(t, x);
+region.print("lake.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;
+
+
+
+