diff --git a/crf-chain2-tiers.cabal b/crf-chain2-tiers.cabal
--- a/crf-chain2-tiers.cabal
+++ b/crf-chain2-tiers.cabal
@@ -1,5 +1,5 @@
 name:               crf-chain2-tiers
-version:            0.5.0
+version:            0.6.0
 synopsis:           Second-order, tiered, constrained, linear conditional random fields
 description:
     The library provides implementation of the second-order, linear
diff --git a/src/Data/CRF/Chain2/Tiers/DAG.hs b/src/Data/CRF/Chain2/Tiers/DAG.hs
--- a/src/Data/CRF/Chain2/Tiers/DAG.hs
+++ b/src/Data/CRF/Chain2/Tiers/DAG.hs
@@ -32,7 +32,7 @@
 
 import           Prelude hiding (Word)
 import           Control.Applicative ((<$>), (<*>))
-import           Control.Monad (when)
+import           Control.Monad (when, guard)
 
 import           System.IO (hSetBuffering, stdout, BufferMode (..))
 import           Data.Maybe (maybeToList)
@@ -43,7 +43,7 @@
 import qualified Data.Number.LogFloat as LogFloat
 import qualified Numeric.SGD.Momentum as SGD
 import qualified Numeric.SGD.LogSigned as L
-import qualified Data.MemoCombinators as Memo
+-- import qualified Data.MemoCombinators as Memo
 
 import           Data.DAG (DAG)
 import qualified Data.DAG as DAG
@@ -244,36 +244,98 @@
 ------------------------------------------------------
 
 
--- | Compute the probability of the DAG, based on the probabilities assigned to
--- different edges and their labels.
-dagProb :: DAG a (X, Y) -> Double
-dagProb dag = sum
-  [ fromEdge edgeID
-  | edgeID <- DAG.dagEdges dag
-  , DAG.isInitialEdge edgeID dag ]
-  where
-    fromEdge =
-      Memo.wrap DAG.EdgeID DAG.unEdgeID Memo.integral fromEdge'
-    fromEdge' edgeID
-      = edgeProb edgeID
-      * fromNode (DAG.endsWith edgeID dag)
-    edgeProb edgeID =
-      let (_x, y) = DAG.edgeLabel edgeID dag
-      in  sum . map (LogFloat.fromLogFloat . snd) $ Core.unY y
-    fromNode nodeID =
-      case DAG.outgoingEdges nodeID dag of
-        [] -> 1
-        xs -> sum (map fromEdge xs)
+-- -- | Compute the probability of the DAG, based on the probabilities assigned to
+-- -- different edges and their labels.
+-- dagProb :: DAG a (X, Y) -> Double
+-- dagProb dag = sum
+--   [ fromEdge edgeID
+--   | edgeID <- DAG.dagEdges dag
+--   , DAG.isInitialEdge edgeID dag ]
+--   where
+--     fromEdge =
+--       Memo.wrap DAG.EdgeID DAG.unEdgeID Memo.integral fromEdge'
+--     fromEdge' edgeID
+--       = edgeProb edgeID
+--       * fromNode (DAG.endsWith edgeID dag)
+--     edgeProb edgeID =
+--       let (_x, y) = DAG.edgeLabel edgeID dag
+--       in  sum . map (LogFloat.fromLogFloat . snd) $ Core.unY y
+--     fromNode nodeID =
+--       case DAG.outgoingEdges nodeID dag of
+--         [] -> 1
+--         xs -> sum (map fromEdge xs)
+-- 
+-- 
+-- -- | Filter out sentences with `dagProb` different from 1.
+-- verifyDataset :: [DAG a (X, Y)] -> [DAG a (X, Y)]
+-- verifyDataset =
+--   filter verify
+--   where
+--     verify dag =
+--       let p = dagProb dag
+--       in  p >= 1 - eps && p <= 1 + eps
+--     eps = 1e-9
 
 
--- | Filter out sentences with `dagProb` different from 1.
+-- | Filter incorrect sentences.
 verifyDataset :: [DAG a (X, Y)] -> [DAG a (X, Y)]
 verifyDataset =
   filter verify
   where
-    verify dag =
-      let p = dagProb dag
-      in  p >= 1 - eps && p <= 1 + eps
+    verify dag = verifyDAG dag == Nothing
+
+
+-- | Verification error.
+data Error
+  = Malformed
+  | Cyclic
+  | SeveralSources [DAG.NodeID]
+  | SeveralTargets [DAG.NodeID]
+  | WrongBalance [DAG.NodeID]
+    -- ^ Nodes for which the total sum of the incoming probabilities does not
+    -- equal the total sum of the outgoing probabilities
+  deriving (Show, Eq, Ord)
+
+
+-- | Check if the DAG satisfies all the desirable properties.
+-- TODO: lot's of code duplication with the `crf-chain1-constrained` library
+-- (only `edgeProb` is different)
+verifyDAG :: DAG a (X, Y) -> Maybe Error
+verifyDAG dag
+  | not (DAG.isOK dag) = Just Malformed
+  | not (DAG.isDAG dag) = Just Cyclic
+  | length sources /= 1 = Just $ SeveralSources sources
+  | length targets /= 1 = Just $ SeveralTargets targets
+  | length wrong > 1 = Just $ WrongBalance wrong
+  | otherwise = Nothing
+  where
+    sources = do
+      node <- DAG.dagNodes dag
+      guard . null $ DAG.ingoingEdges node dag
+      return node
+    targets = do
+      node <- DAG.dagNodes dag
+      guard . null $ DAG.outgoingEdges node dag
+      return node
+    wrong = do
+      node <- DAG.dagNodes dag
+      let ing = DAG.ingoingEdges node dag
+          out = DAG.outgoingEdges node dag
+          ingBalance =
+            if node `elem` sources
+               then 1
+               else sum (map edgeProb ing)
+          outBalance =
+            if node `elem` targets
+               then 1
+               else sum (map edgeProb out)
+      guard . not $ equal ingBalance outBalance
+      return node
+    edgeProb edgeID =
+      let (_x, y) = DAG.edgeLabel edgeID dag
+      in  sum . map (LogFloat.fromLogFloat . snd) $ Core.unY y
+    equal x y =
+      x - eps <= y && x + eps >= y
     eps = 1e-9