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

Stabler - Lx 185/209 2003
7.3 Earley recognition for CFGs
(16) Earley (1968) showed, in effect, how to build an oracle into a chart construction algorithm for any
grammar G =〈Σ,N,→, s〉. With this strategy, the algorithm has the “prefix property,” which means
that, processing a string from left to right, an ungrammatical prefix (i.e. a sequence of words that is not
a prefix of any grammatical string) will be recognized at the the earliest possible point.
For A, B, C ∈ N and some designated s ′ ∈ N, forS,T,U,V ∈ (N ∪ Σ) ∗ , and for input w1 ...wn ∈ Σn ,
(0, 0) : s ′ → [] • s [axiom]
(i, j) : A → S • wj+1T
(i, j + 1) : A → Swj+1 • T
(i, j) : A → S • BT
(j, j) : B →•U
(i, k) : A → S • BT (k,j) : B → U•
(i, j) : A → SB • T
[scan]
[predict] if B:-U and (U = ɛ ∨ U = CV ∨ (U = wj+1V)
[complete]
The input is recognized iff (0,n): S ′ → S• is in the closure of the axioms (in this case, the set of axioms
has just one element) under these inference rules.
Also note that in order to apply the scan rule, we need to be able to tell which word is in the j + 1’th
position.
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