Annals of Operations Research

, Volume 184, Issue 1, pp 179-207

First online:

The weighted Grammar constraint

  • George KatsirelosAffiliated withUniversity of New South Wales and NICTA
  • , Nina NarodytskaAffiliated withUniversity of New South Wales and NICTA Email author 
  • , Toby WalshAffiliated withUniversity of New South Wales and NICTA

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We introduce the WeightedGrammar constraint and propose propagation algorithms based on the CYK parser and the Earley parser. We show that the traces of these algorithms can be encoded as a weighted negation normal form (WNNF), a generalization of NNF that allows nodes to carry weights. Based on this connection, we prove the correctness and complexity of these algorithms. Specifically, these algorithms enforce domain consistency on the WeightedGrammar constraint in time O(n 3). Further, we propose that the WNNF constraint can be decomposed into a set of primitive arithmetic constraint without hindering propagation.


Constraint programming Global constraints Context free grammars Negation normal form