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What makes backreferences impossible in a DFA regular expressions evaluator?Hello all, I've been lurking for a while but this is my first post, so I apologize if I'm offtopic. I have read in papers such as this one that matching regular expressions with a "Thompson's NFA" or DFA makes matching backreferences inefficient (the above paper says it's np complete). Since I've written a regex engine that uses the "Thompson's NFA" algorithm as I understand it that matches backreferences efficiently in most cases, I'm assuming I am misunderstanding either Thompson's NFA or the use cases that can cause exponential runtime. I've made the entire code available here, and I'm pasting the relevant code at the bottom of my post (it is short). Why are backreferences considered impossible with a dfa regex engine? BEGIN RELEVANT CODE  the compiler compiles a regex to a single MatchSequence data RegexOp where MatchEndAnchor :: RegexOp MatchChar :: Char > RegexOp MatchAny :: RegexOp MatchSequence :: [RegexOp] > RegexOp MatchGreedy :: Int > Int > RegexOp > RegexOp  min, max, operation MatchNonGreedy :: Int > Int > RegexOp > RegexOp MatchClass :: [RegexOp] > RegexOp  used for character classes and (....) MatchLookAhead :: RegexOp > RegexOp MatchNegative :: RegexOp > RegexOp MatchBackRef :: Int > RegexOp BeginCapture :: RegexOp EndCapture :: RegexOp deriving (Eq, Show) ...  a possible state, our runtime keeps a list of all possible states by using the List Monad data ReState = ReState { stream :: String ,current_groups :: [String] ,groups :: [String] ,current_match :: String } deriving (Show, Eq) ...  start a new capture  push_capture :: ReState > ReState push_capture state = ReState (stream state) ([] : current_groups state) (groups state) (current_match state) ...  finish the newest capture and add it to our groups  pop_capture :: ReState > ReState pop_capture state = ReState (stream state) (tail $ current_groups state) (groups state ++ [head $ current_groups state]) (current_match state) ...  dfa_mkop is our main execution function, it takes an op and a state  and returns a list of all possible states  dfa_mkop :: RegexOp > ReState > [ReState] ... dfa_mkop (MatchBackRef refnum) state = do g < return $ groups state if length g < refnum then [] else do gval < return $ g !! (refnum  1) st < return $ stream state if length st < length gval then [] else if take (length gval) st == gval then [matched (length gval) state] else [] dfa_mkop BeginCapture state = [push_capture state] dfa_mkop EndCapture state = [pop_capture state] By Brandon Niemczyk at 20080831 20:02  LtU Forum  previous forum topic  next forum topic  other blogs  10614 reads

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