// Thompson Construction+ −
// (needs :load dfa.scala+ −
// :load nfa.scala+ −
// :load enfa.scala)+ −
+ −
+ −
// states for Thompson construction+ −
case class TState(i: Int) extends State+ −
+ −
object TState {+ −
var counter = 0+ −
+ −
def apply() : TState = {+ −
counter += 1;+ −
new TState(counter - 1)+ −
}+ −
}+ −
+ −
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// some types abbreviations+ −
type NFAt = NFA[TState, Char]+ −
type NFAtrans = (TState, Char) :=> Set[TState]+ −
type eNFAtrans = (TState, Option[Char]) :=> Set[TState]+ −
+ −
+ −
// for composing an eNFA transition with a NFA transition+ −
implicit class RichPF(val f: eNFAtrans) extends AnyVal {+ −
def +++(g: NFAtrans) : eNFAtrans = + −
{ case (q, None) => applyOrElse(f, (q, None)) + −
case (q, Some(c)) => applyOrElse(f, (q, Some(c))) | applyOrElse(g, (q, c)) }+ −
}+ −
+ −
+ −
// NFA that does not accept any string+ −
def NFA_ZERO(): NFAt = {+ −
val Q = TState()+ −
NFA(Set(Q), { case _ => Set() }, Set())+ −
}+ −
+ −
// NFA that accepts the empty string+ −
def NFA_ONE() : NFAt = {+ −
val Q = TState()+ −
NFA(Set(Q), { case _ => Set() }, Set(Q))+ −
}+ −
+ −
// NFA that accepts the string "c"+ −
def NFA_CHAR(c: Char) : NFAt = {+ −
val Q1 = TState()+ −
val Q2 = TState()+ −
NFA(Set(Q1), { case (Q1, d) if (c == d) => Set(Q2) }, Set(Q2))+ −
}+ −
+ −
// sequence of two NFAs+ −
def NFA_SEQ(enfa1: NFAt, enfa2: NFAt) : NFAt = {+ −
val new_delta : eNFAtrans = + −
{ case (q, None) if enfa1.fins(q) => enfa2.starts }+ −
+ −
eNFA(enfa1.starts, new_delta +++ enfa1.delta +++ enfa2.delta, + −
enfa2.fins)+ −
}+ −
+ −
// alternative of two NFAs+ −
def NFA_ALT(enfa1: NFAt, enfa2: NFAt) : NFAt = {+ −
val new_delta : NFAtrans = { + −
case (q, c) => applyOrElse(enfa1.delta, (q, c)) | + −
applyOrElse(enfa2.delta, (q, c)) }+ −
val new_fins = (q: TState) => enfa1.fins(q) || enfa2.fins(q)+ −
+ −
NFA(enfa1.starts | enfa2.starts, new_delta, new_fins)+ −
}+ −
+ −
// star of a NFA+ −
def NFA_STAR(enfa: NFAt) : NFAt = {+ −
val Q = TState()+ −
val new_delta : eNFAtrans = + −
{ case (Q, None) => enfa.starts+ −
case (q, None) if enfa.fins(q) => Set(Q) }+ −
+ −
eNFA(Set(Q), new_delta +++ enfa.delta, Set(Q))+ −
}+ −
+ −
+ −
+ −
// regular expressions+ −
abstract class Rexp+ −
case object ZERO extends Rexp // matches nothing+ −
case object ONE extends Rexp // matches the empty string+ −
case class CHAR(c: Char) extends Rexp // matches a character c+ −
case class ALT(r1: Rexp, r2: Rexp) extends Rexp // alternative+ −
case class SEQ(r1: Rexp, r2: Rexp) extends Rexp // sequence+ −
case class STAR(r: Rexp) extends Rexp // star+ −
+ −
+ −
+ −
+ −
// thompson construction + −
def thompson (r: Rexp) : NFAt = r match {+ −
case ZERO => NFA_ZERO()+ −
case ONE => NFA_ONE()+ −
case CHAR(c) => NFA_CHAR(c) + −
case ALT(r1, r2) => NFA_ALT(thompson(r1), thompson(r2))+ −
case SEQ(r1, r2) => NFA_SEQ(thompson(r1), thompson(r2))+ −
case STAR(r1) => NFA_STAR(thompson(r1))+ −
}+ −
+ −
//optional regular expression (one or zero times)+ −
def OPT(r: Rexp) = ALT(r, ONE)+ −
+ −
//n-times regular expression (explicitly expanded)+ −
def NTIMES(r: Rexp, n: Int) : Rexp = n match {+ −
case 0 => ONE+ −
case 1 => r+ −
case n => SEQ(r, NTIMES(r, n - 1))+ −
}+ −
+ −
+ −
def tmatches(r: Rexp, s: String) : Boolean =+ −
thompson(r).accepts(s.toList)+ −
+ −
def tmatches2(r: Rexp, s: String) : Boolean =+ −
thompson(r).accepts2(s.toList)+ −
+ −
// dfa via subset construction+ −
def tmatches_dfa(r: Rexp, s: String) : Boolean =+ −
subset(thompson(r)).accepts(s.toList)+ −
+ −
// Test Cases+ −
+ −
+ −
// the evil regular expression a?{n} a{n}+ −
def EVIL1(n: Int) : Rexp = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))+ −
+ −
// the evil regular expression (a*)*b+ −
val EVIL2 : Rexp = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))+ −
+ −
//for measuring time+ −
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)+ −
}+ −
+ −
// the size of the NFA can be large, + −
// thus slowing down the breadth-first search+ −
+ −
for (i <- 1 to 13) {+ −
println(i + ": " + "%.5f".format(time_needed(2, tmatches(EVIL1(i), "a" * i))))+ −
}+ −
+ −
for (i <- 1 to 100 by 5) {+ −
println(i + " " + "%.5f".format(time_needed(2, tmatches(EVIL2, "a" * i))))+ −
}+ −
+ −
+ −
// the backtracking needed in depth-first search + −
// can be painfully slow+ −
+ −
for (i <- 1 to 8) {+ −
println(i + " " + "%.5f".format(time_needed(2, tmatches2(EVIL2, "a" * i))))+ −
}+ −
+ −
+ −
+ −
// while my thompson-enfa-subset-partial-function-chain+ −
// is probably not the most effcient way to obtain a fast DFA + −
// (the test below should be much faster with a more direct + −
// construction), in general the DFAs can be slow because of + −
// the state explosion in the subset construction+ −
+ −
for (i <- 1 to 13) {+ −
println(i + ": " + "%.5f".format(time_needed(2, tmatches_dfa(EVIL1(i), "a" * i))))+ −
}+ −
+ −
for (i <- 1 to 100 by 5) {+ −
println(i + " " + "%.5f".format(time_needed(2, tmatches_dfa(EVIL2, "a" * i))))+ −
}+ −