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8/12/2019 Lect10 Earley
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600.465 - Intro to NLP - J. Eisner 1
Earleys Algorithm (1970)
Nice combo of our parsing ideas so far:
no restrictions on the form of the grammar:
A B C spoon D x
incremental parsing (left to right, like humans)
left context constrains parsing of subsequent words
so waste less time building impossible things
makes it faster than O(n3) for many grammars
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Overview of Earleys Algorithm
Finds constituents and partial constituents in input
A B C . D E is partial: only the first half of theA
A
B C D E
A B C . D E
D+ =A
B C D E
A B C D . E
i j i k
j k
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Overview of Earleys Algorithm
Proceeds incrementally, left-to-right
Before it reads word 5, it has already built allhypotheses that are consistent with first 4 words
Reads word 5 & attaches it to immediately preceding
hypotheses. Might yield new constituents that are thenattached to hypotheses immediately preceding them
E.g., attaching D toA B C . D E givesA B C D . E
Attaching E to that givesA B C D E .
Now we have a completeA that we can attach tohypotheses immediately preceding theA, etc.
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Our Usual Example Grammar
ROOT S
S NP VP NP PapaNP Det N N caviar
NP NP PP N spoon
VP VP PP V ateVP V NP P with
PP P NP Det the
Det a
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First Try: Recursive Descent
0 ROOT . S0
0 S . NP VP0
0NP
. Papa0
0 NP Papa . 1
0 S NP . VP1
1 VP . VP PP1
1 VP . VP PP1
1 VP . VP PP1
1 VP . VP PP1
oops, stack overflowed
OK, lets pretend that didnt happen.
Lets suppose we didnt see VP VP PP, and used VP V NP instead.
ROOT S VP VP PP NP Papa V ate
S NP VP VP V NP N caviar P with
NP Det N PP P NP N spoon Det the
NP NP PP Det a
0Papa 1ate 2the 3caviar 4with 5a 6spoon 7
goal stack
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First Try: Recursive Descent
1VP . V NP1 after dot = nonterminal, so recursively look for it (predict)
1V . ate 1 after dot = terminal, so look for it in the input (scan)
1 V ate . 2 after dot = nothing, so parents subgoal is completed (attach) 1 VP V . NP2 predict (next subgoal)
2NP . ... 2 do some more parsing and eventually ...
2NP ... . 7 we complete the parents NP subgoal, so attach
1 VP V NP . 7 attach again
0 S NP VP . 7 attach again
ROOT S VP V NP NP Papa V ate
S NP VP VP VP PP N caviar P with
NP Det N PP P NP N spoon Det the
NP NP PP Det a
0Papa 1ate 2the 3caviar 4with 5a 6spoon 7
0 ROOT . S0
0 S . NP VP0
0 NP . Papa 0
0 NP Papa . 1
0 S NP . VP1 after dot = nonterminal, so recursively look for it (predict)
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First Try: Recursive Descent
0 ROOT . S0
0 S . NP VP0
0 NP . Papa 0
0 NP Papa . 1
0 S NP . VP1
1VP . V NP1
1V . ate 1
1 V ate . 2
1 VP V . NP2
2NP . ... 2
2NP ... . 7
1 VP V NP . 7
ROOT S VP V NP NP Papa V ate
S NP VP VP VP PP N caviar P with
NP Det N PP P NP N spoon Det the
NP NP PP Det a
But how about the other parse?
must backtrack to try predictinga different VP rule here instead
0Papa 1ate 2the 3caviar 4with 5a 6spoon 7
implement by function calls:
S() calls NP() and VP(), which recurse
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First Try: Recursive Descent
1VP . V NP1
1V . ate 1
1 V ate . 2
1 VP V . NP2
2NP . ... 2 do some more parsing and eventually ...
2NP ... . 4 ... the correct NP is from 2 to 4 this timebut mi ht we find the one from 2 to 7 instead?
ROOT S VP V NP NP Papa V ate
S NP VP VP VP PP N caviar P with
NP Det N PP P NP N spoon Det the
NP NP PP Det a
wed better backtrack here too!(why?)
0Papa 1ate 2the 3caviar 4with 5a 6spoon 7
0 ROOT . S0
0 S . NP VP0
0 NP . Papa 0
0 NP Papa . 1
0 S NP . VP1
1VP . VP PP1
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First Try: Recursive Descent
1VP . VP PP1
1VP . VP PP1
1VP . VP PP1
oops, stack overflowed
no fix after allmust transform grammar to eliminate left-recursive rules
ROOT S VP V NP NP Papa V ate
S NP VP VP VP PP N caviar P with
NP Det N PP P NP N spoon Det the
NP NP PP Det a
0Papa 1ate 2the 3caviar 4with 5a 6spoon 7
0 ROOT . S0
0 S . NP VP0
0 NP . Papa 0
0 NP Papa . 1
0 S NP . VP1
1VP . VP PP1
1VP . VP PP1
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Use a Parse Table (= Chart)
Earleys algorithm resembles recursive descent, but solvesthe left-recursion problem. No recursive function calls.
Use a parse table as we did in CKY, so we can look upanything weve discovered so far.
Dynamic programming.
Entries in column 5 look like (3, S NP . VP)(but well omit the etc. to save space)
Built while processing word 5
Means that the input substring from 3 to 5matches the initial NP portion of a S NP VP rule
Dot shows how much weve matched as of column 5
Perfectly fine to have entries like (3, S is it . true that S)
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Use a Parse Table (Chart) Entries in column 5 look like (3, S NP . VP)
What does it mean if we have this entry? Unknown right context: Doesntmean well necessarily be
able to find a VP starting at column 5 to complete the S.
Known left context: Does mean that some dotted rule back
in column 3 is looking for an S that starts at 3. So if we actually do find a VP starting at column 5, allowing us to
complete the S, then well be able to attach the S to something.
And when that something is complete, it too will have a customerto itsleft just as in recursive descent!
In short, a top-down (i.e., goal-directed) parser: it chooses to startbuilding a constituent not because of the input but because thatswhat the left context needs. In the spoon, wont build spoon as averb because theres no way to use a verb there.
So any hypothesis in column 5 couldget used in the correct parse,if words 1-5 are continued in just the right way by words 6-n.
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Operation of the Algorithm
Process all hypotheses one at a time in order.
(Current hypothesis is shown in blue, with substring.) This may add to the end of the
to-do list, or try to add again.new hypotheses
old hypotheses
Process a hypothesis according to what followsthe dot just as in recursive descent: If a word, scan input and see if it matches
If a nonterminal, predict ways to match it(well predict blindly, but could reduce # of predictions by
looking ahead k symbols in the input and only makingpredictions that are compatible with this limited right context)
If nothing, then we have a complete constituent, so
attach it to all its customers (shown in purple).
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B C D E
i j
A
(i, A B C . D E)
column j
current hypothesis (incomplete)which action?
One entry (hypothesis)
All entries ending at j stored in column j, as in CKY
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(j, D . bludger)new entry to process later
Predict
B C D E
i j
A
(i, A B C . D E)
column j
current hypothesis (incomplete)
D
j j bludger
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Scan
(i, A B C . D E)
column j
D
j j bludger
(j, D bludger .)
column k
new entry to process later
k=j+1 in this example
Current hypothesis (incomplete)(j, D . bludger)
+ j kbludger = D
j kbludger
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Attach
D
j k
(i, A B C . D E)
column j column k
(j, D bludger .)
current hypothesis (complete)
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Attach
D
j k
B C D E
+
i j
A
(i, A B C . D E)
=
B C D E
i k
A
(i, A B C D . E)
column j column k
(j, D bludger .)
current hypothesis (complete)
customer (incomplete)
new entry to process later
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Our Usual Example GrammarROOT S
S NP VP NP PapaNP Det N N caviar
NP NP PP N spoon
VP VP PP V ateVP V NP P with
PP P NP Det the
Det a
0Papa 1ate 2the 3caviar 4with 5a 6spoon 7
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0
0 ROOT . S
initialize
Remember this stands for (0, ROOT . S)
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0
0 ROOT . S
0 S . NP VP
predict the kind of S we are looking for
Remember this stands for (0, S . NP VP)
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0
0 ROOT . S
0 S . NP VP
0 NP . Det N0 NP . NP PP
0 NP . Papa
predict the kind of NP we are looking for
(actually well look for 3 kinds: any of the 3 will do)
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0
0 ROOT . S
0 S . NP VP
0 NP . Det N0 NP . NP PP
0 NP . Papa
0 Det . the
0 Det . a
predict the kind of Det we are looking for (2 kinds)
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0
0 ROOT . S
0 S . NP VP
0 NP . Det N0 NP . NP PP
0 NP . Papa
0 Det . the
0 Det . a
predict the kind of NP were looking forbut we were already looking for these sodont add duplicate goals! Note that this happened
when we were processing a left-recursive rule.
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0 Papa 1
0 ROOT . S 0 NP Papa .
0 S . NP VP
0 NP . Det N0 NP . NP PP
0 NP . Papa
0 Det . the
0 Det . a
scan: failure
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0 Papa 1
0 ROOT . S 0 NP Papa .
0 S . NP VP
0 NP . Det N0 NP . NP PP
0 NP . Papa
0 Det . the
0 Det . a scan: failure
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0 Papa 1
0 ROOT . S 0 NP Papa .
0 S . NP VP 0 S NP . VP
0 NP . Det N 0 NP NP . PP0 NP . NP PP
0 NP . Papa
0 Det . the
0 Det . a
attach the newly created NP(which starts at 0) to its customers
(incomplete constituents that end at 0and have NP after the dot)
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0 Papa 1
0 ROOT . S 0 NP Papa .
0 S . NP VP 0 S NP . VP
0 NP . Det N 0 NP NP . PP0 NP . NP PP 1 VP . V NP
0 NP . Papa 1 VP . VP PP
0 Det . the
0 Det . a
predict
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0 Papa 1
0 ROOT . S 0 NP Papa .
0 S . NP VP 0 S NP . VP
0 NP . Det N 0 NP NP . PP0 NP . NP PP 1 VP . V NP
0 NP . Papa 1 VP . VP PP
0 Det . the 1 PP . P NP
0 Det . a
predict
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0 Papa 1
0 ROOT . S 0 NP Papa .
0 S . NP VP 0 S NP . VP
0 NP . Det N 0 NP NP . PP0 NP . NP PP 1 VP . V NP
0 NP . Papa 1 VP . VP PP
0 Det . the 1 PP . P NP
0 Det . a 1 V . ate
predict
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0 Papa 1
0 ROOT . S 0 NP Papa .
0 S . NP VP 0 S NP . VP
0 NP . Det N 0 NP NP . PP0 NP . NP PP 1 VP . V NP
0 NP . Papa 1 VP . VP PP
0 Det . the 1 PP . P NP
0 Det . a 1 V . ate
predict
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0 Papa 1
0 ROOT . S 0 NP Papa .
0 S . NP VP 0 S NP . VP
0 NP . Det N 0 NP NP . PP0 NP . NP PP 1 VP . V NP
0 NP . Papa 1 VP . VP PP
0 Det . the 1 PP . P NP
0 Det . a 1 V . ate
1 P . with
predict
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0 Papa 1 ate 2
0 ROOT . S 0 NP Papa . 1 V ate .
0 S . NP VP 0 S NP . VP
0 NP . Det N 0 NP NP . PP0 NP . NP PP 1 VP . V NP
0 NP . Papa 1 VP . VP PP
0 Det . the 1 PP . P NP
0 Det . a 1 V . ate
1 P . with
scan: success!
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0 Papa 1 ate 2
0 ROOT . S 0 NP Papa . 1 V ate .
0 S . NP VP 0 S NP . VP
0 NP . Det N 0 NP NP . PP0 NP . NP PP 1 VP . V NP
0 NP . Papa 1 VP . VP PP
0 Det . the 1 PP . P NP
0 Det . a 1 V . ate
1 P . with scan: failure
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0 Papa 1 ate 2
0 ROOT . S 0 NP Papa . 1 V ate .
0 S . NP VP 0 S NP . VP 1 VP V . NP
0 NP . Det N 0 NP NP . PP0 NP . NP PP 1 VP . V NP
0 NP . Papa 1 VP . VP PP
0 Det . the 1 PP . P NP
0 Det . a 1 V . ate
1 P . with
attach
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0 Papa 1 ate 2
0 ROOT . S 0 NP Papa . 1 V ate .
0 S . NP VP 0 S NP . VP 1 VP V . NP
0 NP . Det N 0 NP NP . PP 2 NP . Det N0 NP . NP PP 1 VP . V NP 2 NP . NP PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa
0 Det . the 1 PP . P NP
0 Det . a 1 V . ate
1 P . with
predict
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0 Papa 1 ate 2
0 ROOT . S 0 NP Papa . 1 V ate .
0 S . NP VP 0 S NP . VP 1 VP V . NP
0 NP . Det N 0 NP NP . PP 2 NP . Det N0 NP . NP PP 1 VP . V NP 2 NP . NP PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa
0 Det . the 1 PP . P NP 2 Det . the
0 Det . a 1 V . ate 2 Det . a
1 P . with
predict (these next few stepsshould look familiar)
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0 Papa 1 ate 2
0 ROOT . S 0 NP Papa . 1 V ate .
0 S . NP VP 0 S NP . VP 1 VP V . NP
0 NP . Det N 0 NP NP . PP 2 NP . Det N0 NP . NP PP 1 VP . V NP 2 NP . NP PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa
0 Det . the 1 PP . P NP 2 Det . the
0 Det . a 1 V . ate 2 Det . a
1 P . with
predict
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0 Papa 1 ate 2
0 ROOT . S 0 NP Papa . 1 V ate .
0 S . NP VP 0 S NP . VP 1 VP V . NP
0 NP . Det N 0 NP NP . PP 2 NP . Det N0 NP . NP PP 1 VP . V NP 2 NP . NP PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa
0 Det . the 1 PP . P NP 2 Det . the
0 Det . a 1 V . ate 2 Det . a
1 P . with
scan (this time we fail sincePapa is not the next word)
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0 Papa 1 ate 2 the 3
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the .
0 S . NP VP 0 S NP . VP 1 VP V . NP
0 NP . Det N 0 NP NP . PP 2 NP . Det N0 NP . NP PP 1 VP . V NP 2 NP . NP PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa
0 Det . the 1 PP . P NP 2 Det . the
0 Det . a 1 V . ate 2 Det . a
1 P . with
scan: success!
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0 Papa 1 ate 2 the 3
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the .
0 S . NP VP 0 S NP . VP 1 VP V . NP
0 NP . Det N 0 NP NP . PP 2 NP . Det N0 NP . NP PP 1 VP . V NP 2 NP . NP PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa
0 Det . the 1 PP . P NP 2 Det . the
0 Det . a 1 V . ate 2 Det . a
1 P . with
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0 Papa 1 ate 2 the 3
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N
0 NP . Det N 0 NP NP . PP 2 NP . Det N0 NP . NP PP 1 VP . V NP 2 NP . NP PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa
0 Det . the 1 PP . P NP 2 Det . the
0 Det . a 1 V . ate 2 Det . a
1 P . with
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0 Papa 1 ate 2 the 3
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon
0 NP . Papa 1 VP . VP PP 2 NP . Papa
0 Det . the 1 PP . P NP 2 Det . the
0 Det . a 1 V . ate 2 Det . a
1 P . with
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0 Papa 1 ate 2 the 3 caviar 4
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon
0 NP . Papa 1 VP . VP PP 2 NP . Papa
0 Det . the 1 PP . P NP 2 Det . the
0 Det . a 1 V . ate 2 Det . a
1 P . with
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0 Papa 1 ate 2 the 3 caviar 4
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon
0 NP . Papa 1 VP . VP PP 2 NP . Papa
0 Det . the 1 PP . P NP 2 Det . the
0 Det . a 1 V . ate 2 Det . a
1 P . with
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0 Papa 1 ate 2 the 3 caviar 4
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon
0 NP . Papa 1 VP . VP PP 2 NP . Papa
0 Det . the 1 PP . P NP 2 Det . the
0 Det . a 1 V . ate 2 Det . a
1 P . with
attach
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0 Papa 1 ate 2 the 3 caviar 4
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP .0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa
0 Det . the 1 PP . P NP 2 Det . the
0 Det . a 1 V . ate 2 Det . a
1 P . with
attach
(again!)
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0 Papa 1 ate 2 the 3 caviar 4
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP .0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP
0 Det . a 1 V . ate 2 Det . a
1 P . with
attach(again!)
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0 Papa 1 ate 2 the 3 caviar 4
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP .0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP
1 P . with
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0 Papa 1 ate 2 the 3 caviar 4
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP .0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP
1 P . with 0 ROOT S .
attach(again!)
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0 Papa 1 ate 2 the 3 caviar 4
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP .0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP
1 P . with 0 ROOT S .
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0 Papa 1 ate 2 the 3 caviar 4
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP .0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP
1 P . with 0 ROOT S .
4 P . with
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0 Papa 1 ate 2 the 3 caviar 4
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP .0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP
1 P . with 0 ROOT S .
4 P . with
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0 Papa 1 ate 2 the 3 caviar 4 with 5
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 4 P with .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP .0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP
1 P . with 0 ROOT S .
4 P . with
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0 Papa 1 ate 2 the 3 caviar 4 with 5
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 4 P with .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP .0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP
1 P . with 0 ROOT S .
4 P . with
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0 Papa 1 ate 2 the 3 caviar 4 with 5
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 4 P with .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 5 NP . Det N0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP . NP PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 5 NP . Papa
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP
1 P . with 0 ROOT S .
4 P . with
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0 Papa 1 ate 2 the 3 caviar 4 with 5
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 4 P with .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 5 NP . Det N
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP . NP PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 5 NP . Papa
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 5 Det . the
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP 5 Det . a
1 P . with 0 ROOT S .
4 P . with
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0 Papa 1 ate 2 the 3 caviar 4 with 5
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 4 P with .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 5 NP . Det N
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP . NP PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 5 NP . Papa
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 5 Det . the
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP 5 Det . a
1 P . with 0 ROOT S .
4 P . with
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0 Papa 1 ate 2 the 3 caviar 4 with 5
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 4 P with .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 5 NP . Det N
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP . NP PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 5 NP . Papa
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 5 Det . the
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP 5 Det . a
1 P . with 0 ROOT S .
4 P . with
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0 Papa 1 ate 2 the 3 caviar 4 with 5
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 4 P with .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 5 NP . Det N
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP . NP PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 5 NP . Papa
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 5 Det . the
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP 5 Det . a
1 P . with 0 ROOT S .
4 P . with
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ate 2 the 3 caviar 4 with 5 a 6
. 1 V ate . 2 Det the . 3 N caviar . 4 P with . 5 Det a .
1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP
P 2 NP . Det N 3 N . caviar 1 VP V NP . 5 NP . Det N
2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP . NP PP
P 2 NP . Papa 0 S NP VP . 5 NP . Papa
2 Det . the 1 VP VP . PP 5 Det . the
2 Det . a 4 PP . P NP 5 Det . a
0 ROOT S .
4 P . with
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ate 2 the 3 caviar 4 with 5 a 6
. 1 V ate . 2 Det the . 3 N caviar . 4 P with . 5 Det a .
1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP 5 NP Det . N
P 2 NP . Det N 3 N . caviar 1 VP V NP . 5 NP . Det N
2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP . NP PP
P 2 NP . Papa 0 S NP VP . 5 NP . Papa
2 Det . the 1 VP VP . PP 5 Det . the
2 Det . a 4 PP . P NP 5 Det . a
0 ROOT S .
4 P . with
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ate 2 the 3 caviar 4 with 5 a 6
. 1 V ate . 2 Det the . 3 N caviar . 4 P with . 5 Det a .
1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP 5 NP Det . N
P 2 NP . Det N 3 N . caviar 1 VP V NP . 5 NP . Det N 6 N . caviar
2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP . NP PP 6 N . spoon
P 2 NP . Papa 0 S NP VP . 5 NP . Papa
2 Det . the 1 VP VP . PP 5 Det . the
2 Det . a 4 PP . P NP 5 Det . a
0 ROOT S .
4 P . with
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ate 2 the 3 caviar 4 with 5 a 6
. 1 V ate . 2 Det the . 3 N caviar . 4 P with . 5 Det a .
1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP 5 NP Det . N
P 2 NP . Det N 3 N . caviar 1 VP V NP . 5 NP . Det N 6 N . caviar
2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP . NP PP 6 N . spoon
P 2 NP . Papa 0 S NP VP . 5 NP . Papa
2 Det . the 1 VP VP . PP 5 Det . the
2 Det . a 4 PP . P NP 5 Det . a
0 ROOT S .
4 P . with
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ate 2 the 3 caviar 4 with 5 a 6 spoon 7
. 1 V ate . 2 Det the . 3 N caviar . 4 P with . 5 Det a . 6 N spoon .
1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP 5 NP Det . N 5 NP Det N .
P 2 NP . Det N 3 N . caviar 1 VP V NP . 5 NP . Det N 6 N . caviar
2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP . NP PP 6 N . spoon
P 2 NP . Papa 0 S NP VP . 5 NP . Papa
2 Det . the 1 VP VP . PP 5 Det . the
2 Det . a 4 PP . P NP 5 Det . a
0 ROOT S .
4 P . with
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ate 2 the 3 caviar 4 with 5 a 6 spoon 7. 1 V ate . 2 Det the . 3 N caviar . 4 P with . 5 Det a . 6 N spoon .
1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP 5 NP Det . N 5 NP Det N .
P 2 NP . Det N 3 N . caviar 1 VP V NP . 5 NP . Det N 6 N . caviar 4 PP P NP .
2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP . NP PP 6 N . spoon 5 NP NP . PP
P 2 NP . Papa 0 S NP VP . 5 NP . Papa
2 Det . the 1 VP VP . PP 5 Det . the
2 Det . a 4 PP . P NP 5 Det . a
0 ROOT S .
4 P . with
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0 Papa 1 ate 2 the 3 caviar 4 with a spoon 70 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 6 N spoon .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 5 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 4 PP P NP .
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 2 NP NP PP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 1 VP VP PP .
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP
1 P . with 0 ROOT S .
4 P . with
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0 Papa 1 ate 2 the 3 caviar 4 with a spoon 70 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 6 N spoon .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 5 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 4 PP P NP .
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 2 NP NP PP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 1 VP VP PP .
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP 7 PP . P NP
1 P . with 0 ROOT S .
4 P . with
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0 Papa 1 ate 2 the 3 caviar 4 with a spoon 70 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 6 N spoon .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 5 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 4 PP P NP .
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 2 NP NP PP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 1 VP VP PP .
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP 7 PP . P NP
1 P . with 0 ROOT S . 1 VP V NP .
4 P . with 2 NP NP . PP
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0 Papa 1 ate 2 the 3 caviar 4 with a spoon 70 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 6 N spoon .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 5 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 4 PP P NP .
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 2 NP NP PP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 1 VP VP PP .
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP 7 PP . P NP
1 P . with 0 ROOT S . 1 VP V NP .
4 P . with 2 NP NP . PP
0 S NP VP .
1 VP VP . PP
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0 Papa 1 ate 2 the 3 caviar 4 with a spoon 70 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 6 N spoon .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 5 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 4 PP P NP .
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 2 NP NP PP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 1 VP VP PP .
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP 7 PP . P NP
1 P . with 0 ROOT S . 1 VP V NP .
4 P . with 2 NP NP . PP
0 S NP VP .
1 VP VP . PP
7 P . with
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0 Papa 1 ate 2 the 3 caviar 4 with a spoon 70 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 6 N spoon .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 5 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 4 PP P NP .
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 2 NP NP PP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 1 VP VP PP .
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP 7 PP . P NP
1 P . with 0 ROOT S . 1 VP V NP .
4 P . with 2 NP NP . PP
0 S NP VP .
1 VP VP . PP
7 P . with
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0 Papa 1 ate 2 the 3 caviar 4 with a spoon 70 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 6 N spoon .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 5 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 4 PP P NP .
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 2 NP NP PP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 1 VP VP PP .
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP 7 PP . P NP
1 P . with 0 ROOT S . 1 VP V NP .
4 P . with 2 NP NP . PP
0 S NP VP .
1 VP VP . PP
7 P . with
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0 Papa 1 ate 2 the 3 caviar 4 with a spoon 70 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 6 N spoon .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 5 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 4 PP P NP .
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 2 NP NP PP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 1 VP VP PP .
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP 7 PP . P NP
1 P . with 0 ROOT S . 1 VP V NP .
4 P . with 2 NP NP . PP
0 S NP VP .
1 VP VP . PP
7 P . with
0 ROOT S .
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0 Papa 1 ate 2 the 3 caviar 4 with a spoon 70 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 6 N spoon .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 5 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 4 PP P NP .
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 2 NP NP PP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 1 VP VP PP .
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP 7 PP . P NP
1 P . with 0 ROOT S . 1 VP V NP .
4 P . with 2 NP NP . PP
0 S NP VP .
1 VP VP . PP
7 P . with
0 ROOT S .
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0 Papa 1 ate 2 the 3 caviar 4 with a spoon 70 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 6 N spoon .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 5 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 4 PP P NP .
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 2 NP NP PP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 1 VP VP PP .
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP 7 PP . P NP
1 P . with 0 ROOT S . 1 VP V NP .
4 P . with 2 NP NP . PP
0 S NP VP .
1 VP VP . PP
7 P . with
0 ROOT S .
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0 Papa 1 ate 2 the 3 caviar 4 with a spoon 70 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 6 N spoon .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 5 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 4 PP P NP .
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 2 NP NP PP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 1 VP VP PP .
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP 7 PP . P NP
1 P . with 0 ROOT S . 1 VP V NP .
4 P . with 2 NP NP . PP
0 S NP VP .
1 VP VP . PP
7 P . with
0 ROOT S .
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Left Recursion Kills Pure
Top-Down Parsing
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600.465 - Intro to NLP - J. Eisner 81
p g
VP
Left Recursion Kills Pure
Top-Down Parsing
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600.465 - Intro to NLP - J. Eisner 82
p g
VP
VP PP
Left Recursion Kills Pure
Top-Down Parsing
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600.465 - Intro to NLP - J. Eisner 83
VP PP
VP
VP PP
Left Recursion Kills Pure
Top-Down Parsing
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600.465 - Intro to NLP - J. Eisner 84
VP PP
VP
VP PP
VP PP
makes new hypothesesad infinitum before weveseen the PPs at all
hypotheses try to predictin advance how manyPPs will arrive in input
but Earleys Alg is Okay!
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600.465 - Intro to NLP - J. Eisner 85
VP
PPVP
1 VP . VP PP
(in column 1)
but Earleys Alg is Okay!
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600.465 - Intro to NLP - J. Eisner 86
VP
V NP
1 VP V NP .
ate the caviar
VP
PPVP
1 VP . VP PP
(in column 1)
(in column 4)
but Earleys Alg is Okay!
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600.465 - Intro to NLP - J. Eisner 87
VP
V NP
VP
PPVP
V NP
attach
ate the caviar
1 VP VP . PP
VP
PPVP
1 VP . VP PP
(in column 1)
(in column 4)
but Earleys Alg is Okay!
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600.465 - Intro to NLP - J. Eisner 88
VP
V NP
VP
PPVP
V NPate the caviar
with a spoon
1 VP VP PP .
VP
PPVP
1 VP . VP PP
(in column 1)
(in column 7)
but Earleys Alg is Okay!
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600.465 - Intro to NLP - J. Eisner 89
VP
V NP
VP
PPVP
V NPate the caviar
with a spoon
1 VP VP PP .
VP
PPVP
1 VP . VP PP
can be reused(in column 1)
(in column 7)
but Earleys Alg is Okay!
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600.465 - Intro to NLP - J. Eisner 90
VP
V NP
VP
PPVP
V NP
VP
PP
1 VP VP . PP
ate the caviar
with a spoon
VP
PPVP
1 VP . VP PP
can be reused(in column 1)
(in column 7)
attach
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but Earleys Alg is Okay!
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600.465 - Intro to NLP - J. Eisner 92
VP
V NP
VP
PPVP
V NP
VP
PP
ate the caviar
with a spoon
in his bed
1 VP VP PP .
VP
PPVP
1 VP . VP PP
can be reused again(in column 1)
(in column 10)
but Earleys Alg is Okay!
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600.465 - Intro to NLP - J. Eisner 93
VP
V NP
VP
PPVP
V NP
VP
PPVP
1 VP . VP PP
can be reused again
VP
PP
VP
PP
1 VP VP . PP
ate the caviar
with a spoon
in his bed
(in column 1)
(in column 10)
attach
0 Papa 1 ate 2 the 3 caviar 4 with a spoon 7
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0 Papa 1 ate 2 the 3 caviar 4 with a spoon 70 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 6 N spoon .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 5 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 4 PP P NP .
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 2 NP NP PP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 1 VP VP PP .
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP 7 PP . P NP1 P . with 0 ROOT S . 1 VP V NP .
4 P . with 2 NP NP . PP
0 S NP VP .
1 VP VP . PP
7 P . with
0 ROOT S .
completed a VP in col 4col 1 lets us use it in a VP PP structure
0 Papa 1 ate 2 the 3 caviar 4 with a spoon 7
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0 Papa 1 ate 2 the 3 caviar 4 with a spoon 70 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 6 N spoon .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 5 NP Det N .
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 4 PP P NP .
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP NP . PP
0 NP . Papa 1 VP . VP PP 2 NP . Papa 0 S NP VP . 2 NP NP PP .
0 Det . the 1 PP . P NP 2 Det . the 1 VP VP . PP 1 VP VP PP.
0 Det . a 1 V . ate 2 Det . a 4 PP . P NP 7 PP . P NP1 P . with 0 ROOT S . 1 VP V NP .
4 P . with 2 NP NP . PP
0 S NP VP .
1 VP VP . PP
7 P . with
0 ROOT S .
completed that VP = VP PP in col 7col 1 would let us use itin a VP PP structurecan reuse col 1 as often as we need
Whats the Complexity?
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600.465 - Intro to NLP - J. Eisner 96
Recommended