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

Stabler - Lx 185/209 2003
6.4 All the GLC parsing methods (the “stack based” methods)
(23) LC parsing uses a rule after establishing its leftmost element. We can represent how much of the right
side is established before the rule is used in the following way:
s:-np][vp
LL parsing uses a rule predictively, without establishing any of the right side:
s:-][np , v p
LR parsing uses a rule conservatively, after establishing all of the right side:
s:-np, vp][
Let’s call the sequence on the right that triggers the use of the rule, the trigger.
In a rule like this with 2 constituents on the right side, these 3 options are the only ones.
This observation is made in Brosgol (1974), and in Demers (1977).
(24) In general, it is clear that with a rule that has n elements on its right side, there are n + 1optionsfor
the parser.
Furthermore, the parser need not treat all rules the same way, so in a grammar like the following, the
number of parsing options is the product of the number of ways to parse each rule.
(25) As Demers (1977) points out, the collection of trigger functions F for any grammar can be naturally
partially ordered by top-downness:
F1 ≤ F2 if and only if for every production p, the trigger F1(p) is at least as long as F2(p).
In other words, a setting of triggers F1 is as bottom-up as F2 if and only if for every production p, the
triggering point defined by F1 is at least as far to the right as the triggering point defined by F2. It is
easy to see that 〈F, ≤〉 is a lattice, as Demers claims, since for any collection F of trigger functions
for any grammar, the least upper bound of F is just the function which maps each rule to the trigger
which is the shortest of the triggers assigned by any function in F, and the greatest lower bound of
F is the function which maps each rule to the trigger which is the longest assigned by any function in
F. Furthermore, the lattice is finite. 25 We call this lattice of recognition strategies the GLC lattice. The
simple lattice structure for a 3 rule grammar can be depicted like this:
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