In the raw grammar, there are many unar ies, and once any major category is constructed overa span, most others become constructible as well us ing unary chains (see Klein and Manning (2001) for discussion) (self citation)

However, the present algorithm and estimates work just as well for top-down chart parsing, given suitable active items as nodes; see (Klein and Manning, 2001a) (self citation)

If one uses b(e, s) to prioritize edges, we show in Kleinand Manning (2001a), that the parser is optimal over ar bitrary PCFGs, and a wide range of control strategies (self citation)

The proof of this is very similar to the proof of the uniform-cost case in Klein and Manning (2001a), and so we omit it for space reasons (it can be found in Klein and Manning, 2002).Concretely, we can use b + a as the edge priority, pro vided a is an admissible, monotonic estimate of ? (self citation)

As discussed in Klein and Manning (2001b), the only source of constraint on what edges can be built where is the tags in the rules (self citation)

This is the method we usedto implement F; exactly parsing with the projected gram mar was much slower and did not result in substantial improvement.It is worth explicitly discussing how the F estimate dif fers from top-down grammar-driven filtering standardly used by top-down chart parsers; in the treebank grammar, there is virtually no top-down filtering to be exploited (again, see Klein and Manning (2001b)) (self citation)

9 Whenever a pattern is successfully found, we add all patterns with m + 1 terminals that are prefixed by it 9Conveniently, the implementation of Chiang (2007) uses aprefix tree grammar encoding, as described in Klein and Manning (2001)

A packed forest (Tomita 1987; Klein and Manning, 2001; Huang and Chiang, 2005) is a compact representation of many possible parse trees of a sentence, which can be for mally described as a triple , where V is the set of non-terminal nodes, E is the set of hy per-edges and S is a sentence represented as an ordered word sequence

The concept of hyper-path and hyper-tree could be viewed as an extension of the "prefix merging" ideas for CFG rules (Klein and Manning 2001)

Before carrying out experimentation, the NoEmpties transformation was applied to all sets (Klein and Manning, 2001).We implemented the CYK-Viterbi parsing al gorithm as the parse engine within the IPP framework

X unary productions for all non-terminals X, (5) collapsing unary chains to a single (possibly composite) unary production (Klein and Manning, 2001), (6) introducing new categories such as AUX (Charniak, 1997), and (7) collapsing of categories such as PRT and ADVP (Collins, 1997)