diff -r bddf14e026b3 -r b5d57d7064bb progs/re3.scala --- 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))*)))