(2) find the highest scoring derivation using dynamic programming

Steps 1 and 2 can be performed efficiently; in particular, we avoid the classical dynamic programming intersection, instead relying on dynamic programming over the original, simple hypergraph.

0 Using dynamic programming , find values for the yv and ye variables that form a valid derivation, and that maximize

The approach uses Lagrangian relaxation to decompose the decoding problem into tractable sub-problems, thereby avoiding exhaustive dynamic programming .

Exact dynamic programming algorithms for the problem are well known (Bar-Hillel et al., 1964), but are too expensive to be used in practice.2 Previous work on decoding for syntax-based SMT has therefore been focused primarily on approximate search methods.

Dynamic programming over the weighted hypergraph.

We do this by gradually introducing constraints to step 1 ( dynamic programming over the hypergraph), while still maintaining efficiency.

The second step involves simple dynamic programming over the hypergraph (V, E) (it is simple to integrate the 68 terms into this algorithm).

The main steps of the algorithm are: 1) construction of the graph (8, T); 2) at each iteration, dynamic programming over the hypergraph (V, E); 3) at each iteration, all-pairs shortest path algorithms over the graph (8, T).

steps—hypergraph dynamic programming , and all-pairs shortest path—are widely known algorithms that are simple to implement.

General algorithms for parsing LCFRSs build a dynamic programming chart of recognized nonterminals bottom-up, in a manner analogous to the CKY algorithm for CFGs (Hopcroft and Ullman, 1979), but with time and space complexity that are dependent on the rank and fanout of the grammar rules.

Whenever it is possible, binarization of LCFRS rules, or reduction of rank to two, is therefore important for parsing, as it reduces the time complexity needed for dynamic programming .

Existing parsing algorithms for LCFRSs exploit dynamic programming .

AS an example, in the case of parsing based on CFGS, nonterminals as well as partial parses all have fanout one, resulting in the standard time complexity of O(|w|3) of dynamic programming methods.