--- a/progs/re3.scala	Mon Feb 13 23:22:45 2017 +0000
+++ b/progs/re3.scala	Wed Mar 15 01:24:39 2017 +0000
@@ -1,3 +1,6 @@
+// Version with simplification during derivatives;
+// this keeps the regular expressions small, which
+// is good for run-time
 
 abstract class Rexp
 case object ZERO extends Rexp
@@ -32,7 +35,7 @@
     else SEQ(der(c, r1), r2)
   case STAR(r1) => SEQ(der(c, r1), STAR(r1))
   case NTIMES(r, i) => 
-    if (i == 0) ZERO else der(c, SEQ(r, NTIMES(r, i - 1)))
+    if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1))
 }
 
 def simp(r: Rexp) : Rexp = r match {
@@ -63,12 +66,12 @@
 def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
 
 
-var regex = NTIMES(CHAR('a'),5)
-println(matcher(regex,"aaaaa"))
-
 //one or zero
 def OPT(r: Rexp) = ALT(r, ONE)
 
+
+// Test Cases
+
 //evil regular expressions
 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))
 val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
@@ -83,20 +86,43 @@
 
 
 //test: (a?{n}) (a{n})
-for (i <- 1 to 9001 by 10) {
+for (i <- 1 to 11001 by 1000) {
   println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))
 }
 
-for (i <- 1 to 9001 by 1000) {
+for (i <- 1 to 11001 by 1000) {
   println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))
 }
 
 //test: (a*)* b
-for (i <- 1 to 7000001 by 500000) {
+for (i <- 1 to 6000001 by 500000) {
+  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i))))
+}
+
+for (i <- 1 to 6000001 by 500000) {
   println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i))))
 }
 
-for (i <- 1 to 7000001 by 500000) {
-  println(i + " " + "%.5f".format(time_needed(2, matcher(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)
+  case NTIMES(r, _) => 1 + size(r)
 }
 
+
+// now the size of the derivatives grows 
+// much, much slower
+
+size(ders("".toList, EVIL2))      // 5
+size(ders("a".toList, EVIL2))     // 8
+size(ders("aa".toList, EVIL2))    // 8
+size(ders("aaa".toList, EVIL2))   // 8
+size(ders("aaaa".toList, EVIL2))  // 8
+size(ders("aaaaa".toList, EVIL2)) // 8