| Efficient Prediction | Variables 20 indicate edges in the parse tree that have been cut in order to remove subtrees . |
| Efficient Prediction | Constraint 9 encodes the requirement that only full subtrees may be deleted. |
| Joint Model | In our complete model, which jointly extracts and compresses sentences, we choose whether or not to cut individual subtrees in the constituency parses |
| Joint Model | This ensures that only subtrees may be deleted. |
| Composed Rule Extraction | In order to ensure that this rule is used during decoding, we must generate subtrees with a height of 7 for CO. |
| Composed Rule Extraction | 4For one (binarized) hyperedge e of a node, suppose there are a: subtrees in the left tail node and y subtrees in the right tail node. |
| Composed Rule Extraction | Then the number of subtrees guided by e is (a: —|— 1) X (y —|— 1). |
| Notation | We also need a substitution that replaces subtrees . |
| Notation | Then t[pi <— 75, | l g i g n] denotes the tree that is obtained from t by replacing (in parallel) the subtrees at pi by ti for every 2' E |
| Preservation of regularity | This is necessary because those two mentioned subtrees must reproduce t1 and 752 from the end of the ‘X’-chain. |