--- a/progs/re1.scala	Tue Sep 26 14:07:29 2017 +0100
+++ b/progs/re1.scala	Tue Sep 26 14:08:49 2017 +0100
@@ -1,3 +1,6 @@
+// Simple matcher for basic regular expressions
+
+object Test {
 
 abstract class Rexp
 case object ZERO extends Rexp                    // matches nothing
@@ -19,6 +22,8 @@
 
 }
 
+}
+
 // derivative of a regular expression w.r.t. a character
 def der (c: Char, r: Rexp) : Rexp = r match {
   case ZERO => ZERO
@@ -40,22 +45,27 @@
 // main matcher function
 def matches(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
 
+
 //examples from the homework
+
 val r = STAR(ALT(SEQ(CHAR('a'), CHAR('b')), CHAR('b')))
 der('a', r)
 der('b', r)
 der('c', r)
 
-//optional (one or zero times)
+//optional regular expression (one or zero times)
 def OPT(r: Rexp) = ALT(r, ONE)
 
-//n-times (explicitly expanded)
+//n-times regular expression (explicitly expanded)
 def NTIMES(r: Rexp, n: Int) : Rexp = n match {
   case 0 => ONE
   case 1 => r
   case n => SEQ(r, NTIMES(r, n - 1))
 }
 
+
+// Test Cases
+
 // the evil regular expression  a?{n} a{n}
 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))
 
@@ -70,6 +80,7 @@
   (end - start)/(i * 1.0e9)
 }
 
+
 //test: (a?{n}) (a{n})
 for (i <- 1 to 20) {
   println(i + ": " + "%.5f".format(time_needed(2, matches(EVIL1(i), "a" * i))))
@@ -88,3 +99,43 @@
   println(i + " " + "%.5f".format(time_needed(2, matches(EVIL2, "a" * i))))
 }
 
+
+
+
+// size of a regular expressions - for testing purposes 
+def size(r: Rexp) : Int = r match {
+  case ZERO => 1
+  case ONE => 1
+  case CHAR(_) => 1
+  case ALT(r1, r2) => 1 + size(r1) + size(r2)
+  case SEQ(r1, r2) => 1 + size(r1) + size(r2)
+  case STAR(r) => 1 + size(r)
+}
+
+// the expicit expansion in EVIL1(n) increases
+// drastically its size
+
+size(EVIL1(1))  // 5
+size(EVIL1(3))  // 17
+size(EVIL1(5))  // 29
+size(EVIL1(7))  // 41
+
+
+// given a regular expression and building successive
+// derivatives might result into bigger and bigger
+// regular expressions...here is an example for this:
+
+val BIG_aux = STAR(ALT(CHAR('a'), CHAR('b')))
+val BIG = SEQ(BIG_aux, SEQ(CHAR('a'),SEQ(CHAR('b'), BIG_aux)))
+
+size(ders("".toList, BIG))              // 13
+size(ders("ab".toList, BIG))            // 51
+size(ders("abab".toList, BIG))          // 112
+size(ders("ababab".toList, BIG))        // 191
+size(ders("abababab".toList, BIG))      // 288
+size(ders("ababababab".toList, BIG))    // 403
+size(ders("abababababab".toList, BIG))  // 536
+
+
+size(ders(("ab" * 200).toList, BIG))    // 366808
+