1 

     2 abstract class Rexp

     3 case object ZERO extends Rexp

     4 case object ONE extends Rexp

     5 case class CHAR(c: Char) extends Rexp

     6 case class ALT(r1: Rexp, r2: Rexp) extends Rexp 

     7 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp 

     8 case class STAR(r: Rexp) extends Rexp 

     9 case class NTIMES(r: Rexp, n: Int) extends Rexp 

    10 case class UPNTIMES(r: Rexp, n: Int) extends Rexp 

    11 

    12 // nullable function: tests whether the regular 

    13 // expression can recognise the empty string

    14 def nullable (r: Rexp) : Boolean = r match {

    15   case ZERO => false

    16   case ONE => true

    17   case CHAR(_) => false

    18   case ALT(r1, r2) => nullable(r1) || nullable(r2)

    19   case SEQ(r1, r2) => nullable(r1) && nullable(r2)

    20   case STAR(_) => true

    21   case NTIMES(r, i) => if (i == 0) true else nullable(r)

    22   case UPNTIMES(r: Rexp, n: Int) => true

    23 }

    24 

    25 // derivative of a regular expression w.r.t. a character

    26 def der (c: Char, r: Rexp) : Rexp = r match {

    27   case ZERO => ZERO

    28   case ONE => ZERO

    29   case CHAR(d) => if (c == d) ONE else ZERO

    30   case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))

    31   case SEQ(r1, r2) => 

    32     if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))

    33     else SEQ(der(c, r1), r2)

    34   case STAR(r1) => SEQ(der(c, r1), STAR(r1))

    35   case NTIMES(r1, i) => 

    36     if (i == 0) ZERO else

    37     if (nullable(r1)) SEQ(der(c, r1), UPNTIMES(r1, i - 1))

    38     else SEQ(der(c, r1), NTIMES(r1, i - 1))

    39   case UPNTIMES(r1, i) => 

    40     if (i == 0) ZERO

    41     else SEQ(der(c, r1), UPNTIMES(r1, i - 1)) 

    42 }

    43 

    44 def simp(r: Rexp) : Rexp = r match {

    45   case ALT(r1, r2) => (simp(r1), simp(r2)) match {

    46     case (ZERO, r2s) => r2s

    47     case (r1s, ZERO) => r1s

    48     case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s)

    49   }

    50   case SEQ(r1, r2) =>  (simp(r1), simp(r2)) match {

    51     case (ZERO, _) => ZERO

    52     case (_, ZERO) => ZERO

    53     case (ONE, r2s) => r2s

    54     case (r1s, ONE) => r1s

    55     case (r1s, r2s) => SEQ(r1s, r2s)

    56   }

    57   case r => r

    58 }

    59 

    60 

    61 // derivative w.r.t. a string (iterates der)

    62 def ders (s: List[Char], r: Rexp) : Rexp = s match {

    63   case Nil => r

    64   case c::s => ders(s, simp(der(c, r)))

    65 }

    66 

    67 

    68 // main matcher function

    69 def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))

    70 

    71 //one or zero

    72 def OPT(r: Rexp) = ALT(r, ONE)

    73 

    74 //evil regular expressions

    75 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))

    76 val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))

    77 

    78 

    79 def time_needed[T](i: Int, code: => T) = {

    80   val start = System.nanoTime()

    81   for (j <- 1 to i) code

    82   val end = System.nanoTime()

    83   (end - start)/(i * 1.0e9)

    84 }

    85 

    86 

    87 //test: (a?{n}) (a{n})

    88 for (i <- 1 to 8001 by 1000) {

    89   println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))

    90 }

    91 

    92 for (i <- 1 to 8001 by 1000) {

    93   println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))

    94 }

    95 

    96 //test: (a*)* b

    97 for (i <- 1 to 7000001 by 500000) {

    98   println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i))))

    99 }

   100 

   101 for (i <- 1 to 7000001 by 500000) {

   102   println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i))))

   103 }

   104