Notes on computational linguistics.pdf - UCLA Department of ...

Stabler - Lx 185/209 2003
It is essentially a “dynamic programming” method and it is included here because of its simplicity.
It is doubtful, however, that it will find practical use, for three reasons:
1. n3 time is too much to allow for parsing.
2. The method uses an amount of space proportional to the square of the input length.
3. The method of the next section (Earley’s algorithm) does at least as well in all respects as
this one, and for many grammars does better.
7.1.1 CKY example 1
ip → dp i1
dp → lambs
i1 → i0 vp
i0 → will
vp → v0 dp
v0 → eat
dp → oats
dp
lambs
The axioms can be regarded as specifying a finite state machine representation of the input:
lambs
0 1
will
Given an n state finite state machine representation of the input, computing the CKY closure can be regarded as filling in
the “upper triangle” of an n × n matrix, from the (empty) diagonal up: 32
2
eat
ip
i0
will
3
oats
i1
v0
eat
4
vp
dp
oats
0 1 2 3 4
0 (0,1):dp
(0,1):lambs (0,4):ip
1 (1,2):i0
(1,2):will (1,4):i1
2 (2,3):v0
(2,3):eat (2,4):vp
3 (3,4):dp
(3,4):oats
4
32 CKY tables and other similar structures of intermediate results are frequently constructed by matrix operations. This idea has been
important in complexity analysis and in attempts to find the fastest possible parsing methods (Valiant, 1975; Lee, 1997). Extensions of
matrix methods to more expressive grammars are considered by Satta (1994) and others.
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