1 // version with explicit an n-times regular expression |
1 // Version with explicit an explicit n-times regular expression; |
2 // this keeps the regular expression small |
2 // this keeps the overall regular expression in the EVIL1 regular |
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3 // expression small |
3 |
4 |
4 abstract class Rexp |
5 abstract class Rexp |
5 case object ZERO extends Rexp |
6 case object ZERO extends Rexp |
6 case object ONE extends Rexp |
7 case object ONE extends Rexp |
7 case class CHAR(c: Char) extends Rexp |
8 case class CHAR(c: Char) extends Rexp |
8 case class ALT(r1: Rexp, r2: Rexp) extends Rexp |
9 case class ALT(r1: Rexp, r2: Rexp) extends Rexp |
9 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
10 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
10 case class STAR(r: Rexp) extends Rexp |
11 case class STAR(r: Rexp) extends Rexp |
11 case class NTIMES(r: Rexp, n: Int) extends Rexp //explicit constructor |
12 case class NTIMES(r: Rexp, n: Int) extends Rexp //explicit constructor for n-times |
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13 |
12 |
14 |
13 def nullable (r: Rexp) : Boolean = r match { |
15 def nullable (r: Rexp) : Boolean = r match { |
14 case ZERO => false |
16 case ZERO => false |
15 case ONE => true |
17 case ONE => true |
16 case CHAR(_) => false |
18 case CHAR(_) => false |
18 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
20 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
19 case STAR(_) => true |
21 case STAR(_) => true |
20 case NTIMES(r, i) => if (i == 0) true else nullable(r) |
22 case NTIMES(r, i) => if (i == 0) true else nullable(r) |
21 } |
23 } |
22 |
24 |
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25 |
23 def der (c: Char, r: Rexp) : Rexp = r match { |
26 def der (c: Char, r: Rexp) : Rexp = r match { |
24 case ZERO => ZERO |
27 case ZERO => ZERO |
25 case ONE => ZERO |
28 case ONE => ZERO |
26 case CHAR(d) => if (c == d) ONE else ZERO |
29 case CHAR(d) => if (c == d) ONE else ZERO |
27 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
30 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
28 case SEQ(r1, r2) => |
31 case SEQ(r1, r2) => |
29 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
32 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
30 else SEQ(der(c, r1), r2) |
33 else SEQ(der(c, r1), r2) |
31 case STAR(r1) => SEQ(der(c, r1), STAR(r1)) |
34 case STAR(r1) => SEQ(der(c, r1), STAR(r1)) |
32 case NTIMES(r1, i) => |
35 case NTIMES(r1, i) => |
33 if (i == 0) ZERO else der(c, SEQ(r1, NTIMES(r1, i - 1))) |
36 if (i == 0) ZERO else SEQ(der(c, r1), NTIMES(r1, i - 1)) |
34 } |
37 } |
35 |
38 |
36 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
39 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
37 case Nil => r |
40 case Nil => r |
38 case c::s => ders(s, der(c, r)) |
41 case c::s => ders(s, der(c, r)) |
39 } |
42 } |
40 |
43 |
41 def matches(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r)) |
44 def matches(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r)) |
42 |
45 |
43 |
46 |
44 //optional: one or zero times |
47 //optional regular expression: one or zero times |
45 def OPT(r: Rexp) = ALT(r, ONE) |
48 def OPT(r: Rexp) = ALT(r, ONE) |
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49 |
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50 |
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51 // Test Cases |
46 |
52 |
47 //evil regular expressions |
53 //evil regular expressions |
48 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n)) |
54 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n)) |
49 val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
55 val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
50 |
56 |
55 (end - start)/(i * 1.0e9) |
61 (end - start)/(i * 1.0e9) |
56 } |
62 } |
57 |
63 |
58 |
64 |
59 //test: (a?{n}) (a{n}) |
65 //test: (a?{n}) (a{n}) |
60 for (i <- 1 to 1001 by 10) { |
66 for (i <- 1 to 1201 by 100) { |
61 println(i + " " + "%.5f".format(time_needed(2, matches(EVIL1(i), "a" * i)))) |
67 println(i + " " + "%.5f".format(time_needed(2, matches(EVIL1(i), "a" * i)))) |
62 } |
68 } |
63 |
69 |
64 for (i <- 1 to 1001 by 10) { |
70 for (i <- 1 to 1201 by 100) { |
65 println(i + " " + "%.5f".format(time_needed(2, matches(EVIL1(i), "a" * i)))) |
71 println(i + " " + "%.5f".format(time_needed(2, matches(EVIL1(i), "a" * i)))) |
66 } |
72 } |
67 |
73 |
68 |
74 |
69 //test: (a*)* b |
75 //test: (a*)* b |
74 for (i <- 1 to 20) { |
80 for (i <- 1 to 20) { |
75 println(i + " " + "%.5f".format(time_needed(2, matches(EVIL2, "a" * i)))) |
81 println(i + " " + "%.5f".format(time_needed(2, matches(EVIL2, "a" * i)))) |
76 } |
82 } |
77 |
83 |
78 |
84 |
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85 |
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86 // size of a regular expressions - for testing purposes |
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87 def size(r: Rexp) : Int = r match { |
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88 case ZERO => 1 |
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89 case ONE => 1 |
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90 case CHAR(_) => 1 |
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91 case ALT(r1, r2) => 1 + size(r1) + size(r2) |
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92 case SEQ(r1, r2) => 1 + size(r1) + size(r2) |
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93 case STAR(r) => 1 + size(r) |
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94 case NTIMES(r, _) => 1 + size(r) |
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95 } |
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96 |
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97 // EVIL1(n) has now a constant size, no matter |
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98 // what n is |
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99 |
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100 size(EVIL1(1)) // 7 |
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101 size(EVIL1(3)) // 7 |
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102 size(EVIL1(5)) // 7 |
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103 size(EVIL1(7)) // 7 |
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104 |
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105 |
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106 // but the size of the derivatives can still grow |
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107 // quite dramatically |
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108 |
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109 size(ders("".toList, EVIL2)) // 5 |
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110 size(ders("a".toList, EVIL2)) // 12 |
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111 size(ders("aa".toList, EVIL2)) // 28 |
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112 size(ders("aaa".toList, EVIL2)) // 58 |
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113 size(ders("aaaa".toList, EVIL2)) // 116 |