--- a/progs/re3.scala Fri Sep 28 13:54:18 2018 +0100
+++ b/progs/re3.scala Sun Sep 30 12:01:14 2018 +0100
@@ -1,4 +1,4 @@
-// Version with simplification during derivatives;
+// A version with simplification of derivatives;
// this keeps the regular expressions small, which
// is good for run-time
@@ -13,31 +13,6 @@
case class NTIMES(r: Rexp, n: Int) extends Rexp
-// string of a regular expressions - for testing purposes
-def string(r: Rexp) : String = r match {
- case ZERO => "0"
- case ONE => "1"
- case CHAR(c) => c.toString
- case ALT(r1, r2) => s"(${string(r1)} + ${string(r2)})"
- case SEQ(CHAR(c), CHAR(d)) => s"${c}${d}"
- case SEQ(ONE, CHAR(c)) => s"1${c}"
- case SEQ(r1, r2) => s"(${string(r1)} ~ ${string(r2)})"
- case STAR(r) => s"(${string(r)})*"
- case NTIMES(r, n) => s"(${string(r)}){${n}}"
-}
-
-// 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)
-}
-
-
// nullable function: tests whether the regular
// expression can recognise the empty string
@@ -65,38 +40,27 @@
if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1))
}
-
-
-def simp(r: Rexp, seen: Set[Rexp]) : (Rexp, Set[Rexp]) = r match {
- case ALT(r1, r2) => {
- val (r1s, seen1) = simp(r1, seen)
- val (r2s, seen2) = simp(r2, seen1)
- (r1s, r2s) match {
- case (ZERO, r2s) => (r2s, seen2)
- case (r1s, ZERO) => (r1s, seen2)
- case (r1s, r2s) => (ALT(r1s, r2s), seen2)
- }
+def simp(r: Rexp) : Rexp = r match {
+ case ALT(r1, r2) => (simp(r1), simp(r2)) match {
+ case (ZERO, r2s) => r2s
+ case (r1s, ZERO) => r1s
+ case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s)
}
- case SEQ(r1, r2) => {
- val (r1s, _) = simp(r1, Set())
- val (r2s, _) = simp(r2, Set())
- if (seen.contains(SEQ(r1s, r2s))) (ZERO, seen)
- else (r1s, r2s) match {
- case (ZERO, _) => (ZERO, seen)
- case (_, ZERO) => (ZERO, seen)
- case (ONE, r2s) => (r2s, seen + r2s)
- case (r1s, ONE) => (r1s, seen + r1s)
- case (r1s, r2s) => (SEQ(r1s, r2s), seen + SEQ(r1s, r2s))
- }
+ case SEQ(r1, r2) => (simp(r1), simp(r2)) match {
+ case (ZERO, _) => ZERO
+ case (_, ZERO) => ZERO
+ case (ONE, r2s) => r2s
+ case (r1s, ONE) => r1s
+ case (r1s, r2s) => SEQ(r1s, r2s)
}
- case r => if (seen.contains(r)) (ZERO, seen) else (r, seen + r)
+ case r => r
}
// derivative w.r.t. a string (iterates der)
def ders (s: List[Char], r: Rexp) : Rexp = s match {
case Nil => r
- case c::s => ders(s, simp(der(c, r), Set())._1)
+ case c::s => ders(s, simp(der(c, r)))
}
@@ -108,75 +72,6 @@
def OPT(r: Rexp) = ALT(r, ONE)
-
-
-
-
-
-
-
-def time_needed[T](i: Int, code: => T) = {
- val start = System.nanoTime()
- for (j <- 1 to i) code
- val end = System.nanoTime()
- (end - start)/(i * 1.0e9)
-}
-
-
-// star example
-val Tstar = STAR(STAR(STAR(CHAR('a'))))
-
-string(ders("".toList, Tstar))
-size(ders("".toList, Tstar)) // 4
-string(ders("a".toList, Tstar))
-size(ders("a".toList, Tstar)) // 11
-string(ders("aa".toList, Tstar))
-size(ders("aa".toList, Tstar)) // 11
-string(ders("aaa".toList, Tstar))
-size(ders("aaa".toList, Tstar)) // 11
-string(ders("aaaa".toList, Tstar))
-size(ders("aaaa".toList, Tstar)) // 11
-string(ders("aaaa".toList, Tstar))
-size(ders("aaaaa".toList, Tstar)) // 11
-string(ders("aaaab".toList, Tstar))
-size(ders("aaaaab".toList, Tstar)) // 1
-
-// test: ("a" | "aa")*
-val EVIL3 = STAR(ALT(CHAR('a'), SEQ(CHAR('a'), CHAR('a'))))
-
-for (i <- 1 to 100 by 1) {
- println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL3, "a" * i))) +
- " size: " + size(ders(("a" * i).toList, EVIL3)))
-}
-
-
-println("start " + string(EVIL3) + " " + size(EVIL3))
-val t1 = der('a', EVIL3)
-println(string(t1) + " " + size(t1))
-val t1s = simp(t1, Set())._1
-println("simplified " + string(t1s) + " " + size(t1s))
-val t2 = der('a', t1s)
-println(string(t2) + " " + size(t2))
-val t2s = simp(t2, Set())._1
-println("simplified " + string(t2s) + " " + size(t2s))
-val t3 = der('a', t2s)
-println(string(t3) + " " + size(t3))
-val t3s = simp(t3, Set())._1
-println("simplified " + string(t3s) + " " + size(t3s))
-val t4 = der('a', t3s)
-val t4s = simp(t4, Set())._1
-
-
-
-
-
-
-
-
-println(string(t4) + " " + size(t4))
-println("simplified " + string(t4s) + " " + size(t4s))
-
-
// Test Cases
//evil regular expressions: (a?){n} a{n} and (a*)* b
@@ -193,11 +88,11 @@
//test: (a?{n}) (a{n})
-for (i <- 1 to 8001 by 1000) {
+for (i <- 1 to 7001 by 1000) {
println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))
}
-for (i <- 1 to 8001 by 1000) {
+for (i <- 1 to 7001 by 1000) {
println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))
}
@@ -211,7 +106,6 @@
}
-
// size of a regular expressions - for testing purposes
def size(r: Rexp) : Int = r match {
case ZERO => 1
@@ -235,28 +129,13 @@
size(ders("aaaaa".toList, EVIL2)) // 8
+// test: ("a" | "aa")*
+val EVIL3 = STAR(ALT(CHAR('a'), SEQ(CHAR('a'), CHAR('a'))))
+
+for (i <- 1 to 29 by 1) {
+ println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL3, "a" * i))) +
+ " size: " + size(ders(("a" * i).toList, EVIL3)))
+}
-// Examples from the Sulzmann paper
-val sulzmann = STAR(ALT(ALT(CHAR('a'), CHAR('b')), SEQ(CHAR('a'), CHAR('b'))))
-
-
-for (i <- 1 to 4501 by 500) {
- println(i + ": " + "%.5f".format(time_needed(1, matcher(sulzmann, "a" * i))))
-}
-
-for (i <- 1 to 4501 by 500) {
- println(i + ": " + "%.5f".format(time_needed(1, matcher(sulzmann, "ab" * i))))
-}
-
-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
-
-
-
-(((1 + 1a) ~ ((a + aa))*) + (((0 + 1) ~ ((a + aa))*) + ((1 + 1a) ~ ((a + aa))*)))