diff --git a/src/GF/Data/Utilities.hs b/src/GF/Data/Utilities.hs
index d7e6be2f0..50d1f5195 100644
--- a/src/GF/Data/Utilities.hs
+++ b/src/GF/Data/Utilities.hs
@@ -34,11 +34,6 @@ lookupList a [] = []
 lookupList a (p:ps) | a == fst p = snd p : lookupList a ps
 		    | otherwise  =         lookupList a ps
 
--- | Find the first list in a list of lists
---   which contains the argument.
-findSet :: Eq c => c -> [[c]] -> Maybe [c]
-findSet x = find (x `elem`)
-
 split :: [a] -> ([a], [a])
 split (x : y : as) = (x:xs, y:ys)
     where (xs, ys) = split as
diff --git a/src/GF/Speech/CFGToFiniteState.hs b/src/GF/Speech/CFGToFiniteState.hs
index 89ec88872..25790786a 100644
--- a/src/GF/Speech/CFGToFiniteState.hs
+++ b/src/GF/Speech/CFGToFiniteState.hs
@@ -15,6 +15,10 @@
 module GF.Speech.CFGToFiniteState (cfgToFA, makeSimpleRegular) where
 
 import Data.List
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.Set (Set)
+import qualified Data.Set as Set
 
 import GF.Data.Utilities
 import GF.Formalism.CFG 
@@ -27,13 +31,19 @@ import GF.Speech.FiniteState
 import GF.Speech.Relation
 import GF.Speech.TransformCFG
 
-import Debug.Trace
+data MutRecSet = MutRecSet {
+                            mrCats :: [Cat_],
+                            mrNonRecRules :: [CFRule_],
+                            mrRecRules :: [CFRule_],
+                            mrIsRightRec :: Bool
+                           }
+
+
+type MutRecSets = Map Cat_ MutRecSet
 
 cfgToFA :: Options -> CGrammar -> DFA String
 cfgToFA opts = minimize . compileAutomaton start . makeSimpleRegular
---cfgToFA opts = trfa "minimal" . minimize . trfa "initial" . compileAutomaton start . makeSimpleRegular
   where start = getStartCat opts
-        trfa s fa = trace (s ++ ", states: " ++ show (length (states fa)) ++ ", transitions: " ++ show (length (transitions fa))) fa
 
 makeSimpleRegular :: CGrammar -> CFRules
 makeSimpleRegular = makeRegular . removeIdenticalRules . removeEmptyCats . cfgToCFRules
@@ -45,8 +55,9 @@ makeSimpleRegular = makeRegular . removeIdenticalRules . removeEmptyCats . cfgTo
 makeRegular :: CFRules -> CFRules
 makeRegular g = groupProds $ concatMap trSet (mutRecCats True g)
   where trSet cs | allXLinear cs rs = rs
-                 | otherwise = concatMap handleCat cs
-            where rs = catSetRules g cs
+                 | otherwise = concatMap handleCat csl
+            where csl = Set.toList cs 
+                  rs = catSetRules g csl
                   handleCat c = [CFRule c' [] (mkName (c++"-empty"))] -- introduce A' -> e
                                 ++ concatMap (makeRightLinearRules c) (catRules g c)
                       where c' = newCat c
@@ -62,7 +73,7 @@ makeRegular g = groupProds $ concatMap trSet (mutRecCats True g)
 -- | Get the sets of mutually recursive non-terminals for a grammar.
 mutRecCats :: Bool    -- ^ If true, all categories will be in some set.
                       --   If false, only recursive categories will be included.
-           -> CFRules -> [[Cat_]]
+           -> CFRules -> [Set Cat_]
 mutRecCats incAll g = equivalenceClasses $ refl $ symmetricSubrelation $ transitiveClosure r
   where r = mkRel [(c,c') | (_,rs) <- g, CFRule c ss _ <- rs, Cat c' <- ss]
         allCats = map fst g
@@ -72,67 +83,88 @@ mutRecCats incAll g = equivalenceClasses $ refl $ symmetricSubrelation $ transit
 compileAutomaton :: Cat_ -- ^ Start category
                  -> CFRules
                  -> NFA Token
-compileAutomaton start g = make_fa s [Cat start] f fa''
+compileAutomaton start g = make_fa (g,ns) s [Cat start] f fa''
   where 
   fa = newFA ()
   s = startState fa
   (fa',f) = newState () fa
   fa'' = addFinalState f fa'
-  ns = mutRecCats False g
-  -- | The make_fa algorithm from \"Regular approximation of CFLs: a grammatical view\",
-  --   Mark-Jan Nederhof. International Workshop on Parsing Technologies, 1997.
-  make_fa :: State -> [Symbol Cat_ Token] -> State 
+  ns = mutRecSets g $ mutRecCats False g
+
+mutRecSets :: CFRules -> [Set Cat_] -> MutRecSets
+mutRecSets g = Map.fromList . concatMap mkMutRecSet
+  where 
+  mkMutRecSet cs = [ (c,ms) | c <- csl ]
+   where csl = Set.toList cs
+         rs = catSetRules g csl
+         (nrs,rrs) = partition (ruleIsNonRecursive cs) rs
+         ms = MutRecSet {
+                         mrCats = csl,
+                         mrNonRecRules = nrs,
+                         mrRecRules = rrs,
+                         mrIsRightRec = all (isRightLinear cs) rrs
+                        }
+
+-- | The make_fa algorithm from \"Regular approximation of CFLs: a grammatical view\",
+--   Mark-Jan Nederhof. International Workshop on Parsing Technologies, 1997.
+make_fa :: (CFRules,MutRecSets) -> State -> [Symbol Cat_ Token] -> State 
           -> NFA Token -> NFA Token
-  make_fa q0 alpha q1 fa = 
+make_fa c@(g,ns) q0 alpha q1 fa = 
      case alpha of
         []       -> newTransition q0 q1 Nothing fa
         [Tok t]  -> newTransition q0 q1 (Just t) fa
-        [Cat a]  -> case findSet a ns of
+        [Cat a]  -> case Map.lookup a ns of
                         -- a is recursive
-                        Just ni -> let (fa',ss) = addStatesForCats ni fa
-                                       getState x = lookup' x ss
-                                       niRules = catSetRules g ni
-                                       (nrs,rs) = partition (ruleIsNonRecursive ni) niRules
-                                    in if all (isRightLinear ni) niRules 
-                                        then
-                                         -- the set Ni is right-recursive or cyclic
-                                         let fa''  = foldFuns [make_fa (getState c) xs q1 | CFRule c xs _ <- nrs] fa'
-                                             fa''' = foldFuns [make_fa (getState c) xs (getState d) | CFRule c ss _ <- rs, 
-                                                               let (xs,Cat d) = (init ss,last ss)] fa''
-                                          in newTransition q0 (getState a) Nothing fa'''
-                                        else
-                                        -- the set Ni is left-recursive
-                                         let fa''  = foldFuns [make_fa q0 xs (getState c) | CFRule c xs _ <- nrs] fa'
-                                             fa''' = foldFuns [make_fa (getState d) xs (getState c) | CFRule c (Cat d:xs) _ <- rs] fa''
-                                          in newTransition (getState a) q1 Nothing fa'''
+                        Just n@(MutRecSet { mrCats = ni, mrNonRecRules = nrs, mrRecRules = rs} ) -> 
+                              if mrIsRightRec n
+                               then
+                                -- the set Ni is right-recursive or cyclic
+                                let fa''  = foldl (\ f (CFRule c xs _) -> make_fa_ (getState c) xs q1 f) fa' nrs
+                                    fa''' = foldl (\ f (CFRule c ss _) -> 
+                                                       let (xs,Cat d) = (init ss,last ss)
+                                                        in make_fa_ (getState c) xs (getState d) f) fa'' rs
+                                 in newTransition q0 (getState a) Nothing fa'''
+                               else
+                                -- the set Ni is left-recursive
+                                let fa'' = foldl (\f (CFRule c xs _) -> make_fa_ q0 xs (getState c) f) fa' nrs
+                                    fa''' = foldl (\f (CFRule c (Cat d:xs) _) -> make_fa_ (getState d) xs (getState c) f) fa'' rs
+                                in newTransition (getState a) q1 Nothing fa'''
+                          where
+                          (fa',ss) = addStatesForCats ni fa
+                          getState x = lookup' x ss
                         -- a is not recursive
                         Nothing -> let rs = catRules g a
-                                    in foldl (\fa -> \ (CFRule _ b _) -> make_fa q0 b q1 fa) fa rs
+                                    in foldl (\fa -> \ (CFRule _ b _) -> make_fa_ q0 b q1 fa) fa rs
         (x:beta) -> let (fa',q) = newState () fa
-                     in make_fa q beta q1 $ make_fa q0 [x] q fa'
-  addStatesForCats [] fa = (fa,[])
-  addStatesForCats (c:cs) fa = let (fa',s) = newState () fa
-                                   (fa'',ss) = addStatesForCats cs fa'
-                                in (fa'',(c,s):ss)
-  ruleIsNonRecursive cs = noCatsInSet cs . ruleRhs
+                     in make_fa_ q beta q1 $! make_fa_ q0 [x] q fa'
+  where
+  make_fa_ = make_fa c
+
+addStatesForCats :: [Cat_] -> NFA Token -> (NFA Token, [(Cat_,State)])
+addStatesForCats cs fa = (fa', zip cs (map fst ns))
+  where (fa', ns) = newStates (replicate (length cs) ()) fa
+
+ruleIsNonRecursive :: Set Cat_ -> CFRule_ -> Bool
+ruleIsNonRecursive cs = noCatsInSet cs . ruleRhs
 
 
-noCatsInSet :: Eq c => [c] -> [Symbol c t] -> Bool
+
+noCatsInSet :: Set Cat_ -> [Symbol Cat_ t] -> Bool
 noCatsInSet cs = not . any (`catElem` cs)
 
 -- | Check if all the rules are right-linear, or all the rules are
 --   left-linear, with respect to given categories.
-allXLinear :: Eq c => [c] -> [CFRule c n t] -> Bool
+allXLinear :: Set Cat_ -> [CFRule_] -> Bool
 allXLinear cs rs = all (isRightLinear cs) rs || all (isLeftLinear cs) rs
 
 -- | Checks if a context-free rule is right-linear.
-isRightLinear :: Eq c => [c]  -- ^ The categories to consider
-              -> CFRule c n t -- ^ The rule to check for right-linearity
+isRightLinear :: Set Cat_  -- ^ The categories to consider
+              -> CFRule_   -- ^ The rule to check for right-linearity
               -> Bool
 isRightLinear cs = noCatsInSet cs . safeInit . ruleRhs
 
 -- | Checks if a context-free rule is left-linear.
-isLeftLinear ::  Eq c => [c]  -- ^ The categories to consider
-              -> CFRule c n t -- ^ The rule to check for right-linearity
+isLeftLinear ::  Set Cat_  -- ^ The categories to consider
+              -> CFRule_   -- ^ The rule to check for right-linearity
               -> Bool
 isLeftLinear cs = noCatsInSet cs . drop 1 . ruleRhs
diff --git a/src/GF/Speech/FiniteState.hs b/src/GF/Speech/FiniteState.hs
index dfd5d941d..a2f8952cb 100644
--- a/src/GF/Speech/FiniteState.hs
+++ b/src/GF/Speech/FiniteState.hs
@@ -16,7 +16,8 @@ module GF.Speech.FiniteState (FA, State, NFA, DFA,
 			      states, transitions,
 			      newFA, 
 			      addFinalState,
-			      newState, newTransition,
+			      newState, newStates,
+                              newTransition,
 			      mapStates, mapTransitions,
                               oneFinalState,
 			      moveLabelsToNodes, minimize,
@@ -65,6 +66,10 @@ newState :: a -> FA n a b -> (FA n a b, n)
 newState x (FA g s ss) = (FA g' s ss, n)
     where (g',n) = newNode x g
 
+newStates :: [a] -> FA n a b -> (FA n a b, [(n,a)])
+newStates xs (FA g s ss) = (FA g' s ss, ns)
+    where (g',ns) = newNodes xs g
+
 newTransition :: n -> n -> b -> FA n a b -> FA n a b
 newTransition f t l = onGraph (newEdge (f,t,l))
 
diff --git a/src/GF/Speech/Graph.hs b/src/GF/Speech/Graph.hs
index 2f80ef0ca..7ebecdc34 100644
--- a/src/GF/Speech/Graph.hs
+++ b/src/GF/Speech/Graph.hs
@@ -13,7 +13,7 @@
 -----------------------------------------------------------------------------
 module GF.Speech.Graph ( Graph(..), Node, Edge, Incoming, Outgoing
                         , newGraph, nodes, edges
-                        , nmap, emap, newNode, newEdge, newEdges
+                        , nmap, emap, newNode, newNodes, newEdge, newEdges
                         , incoming, outgoing, getOutgoing
                         , getFrom, getTo, getLabel
                         , reverseGraph, renameNodes
@@ -52,6 +52,11 @@ emap f (Graph c ns es) = Graph c ns [(x,y,f l) | (x,y,l) <- es]
 newNode :: a -> Graph n a b -> (Graph n a b,n)
 newNode l (Graph (c:cs) ns es) = (Graph cs ((c,l):ns) es, c)
 
+newNodes :: [a] -> Graph n a b -> (Graph n a b,[Node n a])
+newNodes ls (Graph cs ns es) = (Graph cs' (ns'++ns) es, ns')
+  where (xs,cs') = splitAt (length ls) cs
+        ns' = zip xs ls
+
 newEdge :: Edge n b -> Graph n a b -> Graph n a b
 newEdge e (Graph c ns es) = Graph c ns (e:es)
 
diff --git a/src/GF/Speech/Relation.hs b/src/GF/Speech/Relation.hs
index 2ad3faccb..c66a07d10 100644
--- a/src/GF/Speech/Relation.hs
+++ b/src/GF/Speech/Relation.hs
@@ -100,10 +100,10 @@ purgeEmpty r = Map.filter (not . Set.null) r
 
 
 -- | Get the equivalence classes from an equivalence relation. 
-equivalenceClasses :: Ord a => Rel a -> [[a]]
+equivalenceClasses :: Ord a => Rel a -> [Set a]
 equivalenceClasses r = equivalenceClasses_ (Map.keys r) r
  where equivalenceClasses_ [] _ = []
-       equivalenceClasses_ (x:xs) r = Set.toList ys:equivalenceClasses_ zs r
+       equivalenceClasses_ (x:xs) r = ys:equivalenceClasses_ zs r
 	   where ys = allRelated r x
                  zs = [x' | x' <- xs, not (x' `Set.member` ys)]
 
diff --git a/src/GF/Speech/TransformCFG.hs b/src/GF/Speech/TransformCFG.hs
index 39060206b..2c920cbda 100644
--- a/src/GF/Speech/TransformCFG.hs
+++ b/src/GF/Speech/TransformCFG.hs
@@ -37,6 +37,8 @@ import Control.Monad
 import Data.FiniteMap
 import Data.List
 import Data.Maybe (fromJust, fromMaybe)
+import Data.Set (Set)
+import qualified Data.Set as Set
 
 
 -- | not very nice to replace the structured CFCat type with a simple string
@@ -134,8 +136,8 @@ ruleFun :: CFRule_ -> Fun
 ruleFun (CFRule _ _ n) = name2fun n 
 
 -- | Checks if a symbol is a non-terminal of one of the given categories.
-catElem :: Eq c => Symbol c t -> [c] -> Bool
-catElem s cs = symbol (`elem` cs) (const False) s
+catElem :: Symbol Cat_ t -> Set Cat_ -> Bool
+catElem s cs = symbol (`Set.member` cs) (const False) s
 
 -- | Check if any of the categories used on the right-hand side
 --   are in the given list of categories.