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

Stabler - Lx 185/209 2003
6.5.2 Bottom-up oracles: lookahead
(44) In top-down parsing, there is no point in using an expansion p:-q, r if the next symbol to be parsed
could not possibly be the beginning of a q.
To guide top-down steps, it would be useful to know what symbol (or what k symbols) are next, waiting
to be parsed. This “bottom-up” information canbeprovidedwitha“lookaheadoracle.”
Obviously, the “lookahead” oracle does not look into the future to hear what has not been spoken yet.
Rather, structure building waits for a word (or in general, k words) to be heard.
Again, we will precompute, for each category p, what the first k symbols of the string could be when
we are recognizing that category in a successful derivation of any sentence.
(45) In calculating lookahead, we ignore the triggers.
One kind of situation that we must allow for is this. If p:-q1,...,qn and q1,...,qi ⇒∗ ɛ, then every next
symbol for qi+1 is a next symbol for p.
(46) For any S ∈ Σ∗ ,letfirstk(S) be the first k symbols of S if |S| ≥k, and otherwise firstk(S) = S.
We can use the following reasoning to calculate all of the next k words that can be waiting to be parsed
as each category symbol is expanded. For some k>0:
wLAw [axiom] if w ∈ Σ
xLAp [axiom]
x1LAq1 ... xnLAqn
xLAp
if p:-q1,...,qn
and either x = q1,...,qk ∈ Σ k for k ≤ n, or x = q1,...,qn ∈ Σ n for n