|
1 // A Version with an explicit n-times regular expression; |
|
2 // this keeps the size of the regular expression in the |
|
3 // EVIL1 test-case quite small |
|
4 // |
|
5 // call the test cases with X = {1,2} |
|
6 // |
|
7 // amm re2.sc testX |
|
8 // |
|
9 // or |
|
10 // |
|
11 // amm re2.sc all |
|
12 |
|
13 |
|
14 abstract class Rexp |
|
15 case object ZERO extends Rexp |
|
16 case object ONE extends Rexp |
|
17 case class CHAR(c: Char) extends Rexp |
|
18 case class ALT(r1: Rexp, r2: Rexp) extends Rexp |
|
19 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
|
20 case class STAR(r: Rexp) extends Rexp |
|
21 case class NTIMES(r: Rexp, n: Int) extends Rexp //explicit constructor for n-times |
|
22 |
|
23 |
|
24 def nullable (r: Rexp) : Boolean = r match { |
|
25 case ZERO => false |
|
26 case ONE => true |
|
27 case CHAR(_) => false |
|
28 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
|
29 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
|
30 case STAR(_) => true |
|
31 case NTIMES(r, i) => if (i == 0) true else nullable(r) |
|
32 } |
|
33 |
|
34 |
|
35 def der (c: Char, r: Rexp) : Rexp = r match { |
|
36 case ZERO => ZERO |
|
37 case ONE => ZERO |
|
38 case CHAR(d) => if (c == d) ONE else ZERO |
|
39 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
|
40 case SEQ(r1, r2) => |
|
41 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
|
42 else SEQ(der(c, r1), r2) |
|
43 case STAR(r1) => SEQ(der(c, r1), STAR(r1)) |
|
44 case NTIMES(r1, i) => |
|
45 if (i == 0) ZERO else SEQ(der(c, r1), NTIMES(r1, i - 1)) |
|
46 } |
|
47 |
|
48 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
|
49 case Nil => r |
|
50 case c::s => ders(s, der(c, r)) |
|
51 } |
|
52 |
|
53 def matcher(r: Rexp, s: String) : Boolean = |
|
54 nullable(ders(s.toList, r)) |
|
55 |
|
56 |
|
57 // the optional regular expression: one or zero times |
|
58 // this regular expression is still defined in terms of ALT |
|
59 def OPT(r: Rexp) = ALT(r, ONE) |
|
60 |
|
61 |
|
62 // Test Cases |
|
63 |
|
64 // evil regular expressions |
|
65 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n)) |
|
66 val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
|
67 |
|
68 def time_needed[T](i: Int, code: => T) = { |
|
69 val start = System.nanoTime() |
|
70 for (j <- 1 to i) code |
|
71 val end = System.nanoTime() |
|
72 (end - start) / (i * 1.0e9) |
|
73 } |
|
74 |
|
75 |
|
76 |
|
77 // test: (a?{n}) (a{n}) |
|
78 @doc("Test (a?{n}) (a{n})") |
|
79 @main |
|
80 def test1() = { |
|
81 for (i <- 0 to 1000 by 100) { |
|
82 println(f"$i: ${time_needed(2, matcher(EVIL1(i), "a" * i))}%.5f") |
|
83 } |
|
84 } |
|
85 |
|
86 // test: (a*)* b |
|
87 @doc("Test (a*)* b") |
|
88 @main |
|
89 def test2() = { |
|
90 for (i <- 0 to 20) { |
|
91 println(f"$i: ${time_needed(2, matcher(EVIL2, "a" * i))}%.5f") |
|
92 } |
|
93 } |
|
94 |
|
95 // the size of a regular expressions - for testing purposes |
|
96 def size(r: Rexp) : Int = r match { |
|
97 case ZERO => 1 |
|
98 case ONE => 1 |
|
99 case CHAR(_) => 1 |
|
100 case ALT(r1, r2) => 1 + size(r1) + size(r2) |
|
101 case SEQ(r1, r2) => 1 + size(r1) + size(r2) |
|
102 case STAR(r) => 1 + size(r) |
|
103 case NTIMES(r, _) => 1 + size(r) |
|
104 } |
|
105 |
|
106 // EVIL1(n) has now a constant size, no matter |
|
107 // what n is; also the derivative only grows |
|
108 // moderately |
|
109 |
|
110 size(EVIL1(1)) // 7 |
|
111 size(EVIL1(3)) // 7 |
|
112 size(EVIL1(5)) // 7 |
|
113 size(EVIL1(7)) // 7 |
|
114 size(EVIL1(20)) // 7 |
|
115 |
|
116 size(ders("".toList, EVIL1(5))) // 7 |
|
117 size(ders("a".toList, EVIL1(5))) // 16 |
|
118 size(ders("aa".toList, EVIL1(5))) // 35 |
|
119 size(ders("aaa".toList, EVIL1(5))) // 59 |
|
120 size(ders("aaaa".toList, EVIL1(5))) // 88 |
|
121 size(ders("aaaaa".toList, EVIL1(5))) // 122 |
|
122 size(ders("aaaaaa".toList, EVIL1(5))) // 151 |
|
123 |
|
124 // but the size of the derivatives can still grow |
|
125 // quite dramatically in case of EVIL2 |
|
126 |
|
127 size(ders("".toList, EVIL2)) // 5 |
|
128 size(ders("a".toList, EVIL2)) // 12 |
|
129 size(ders("aa".toList, EVIL2)) // 28 |
|
130 size(ders("aaa".toList, EVIL2)) // 58 |
|
131 size(ders("aaaa".toList, EVIL2)) // 116 |
|
132 size(ders("aaaaa".toList, EVIL2)) // 230 |
|
133 size(ders("aaaaaa".toList, EVIL2)) // 456 |
|
134 |
|
135 size(ders(("a" * 20).toList, EVIL2)) // 7340068 |
|
136 |
|
137 |
|
138 |
|
139 @doc("All tests.") |
|
140 @main |
|
141 def all() = { test1(); test2() } |