600.465 - intro to nlp - j. eisner1 earley’s algorithm (1970) nice combo of our parsing ideas so...
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600.465 - Intro to NLP - J. Eisner 1
Earley’s 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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600.465 - Intro to NLP - J. Eisner 2
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600.465 - Intro to NLP - J. Eisner 3
Overview of Earley’s Algorithm
Finds constituents and partial constituents in input A B C . D E is partial: only the first half of the A
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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600.465 - Intro to NLP - J. Eisner 4
Overview of Earley’s Algorithm
Proceeds incrementally, left-to-right Before it reads word 5, it has already built all
hypotheses that are consistent with first 4 words Reads word 5 & attaches it to immediately
preceding hypotheses. Might yield new constituents that are then attached to hypotheses immediately preceding them …
E.g., attaching D to A B C . D E gives A B C D . E Attaching E to that gives A B C D E . Now we have a complete A that we can attach to
hypotheses immediately preceding the A, etc.
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600.465 - Intro to NLP - J. Eisner 5
Our Usual Example Grammar
ROOT SS NP VP NP PapaNP Det N N caviarNP NP PP N spoonVP VP PP V ateVP V NP P withPP P NP Det the
Det a
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600.465 - Intro to NLP - J. Eisner 6
First Try: Recursive Descent
0 ROOT . S 0 0 S . NP VP 0
0 NP . Papa 0 0 NP Papa . 1
0 S NP . VP 1 1 VP . VP PP 1
1 VP . VP PP 1 1 VP . VP PP 1 1 VP . VP PP 1
oops, stack overflowed OK, let’s pretend that didn’t happen. Let’s suppose we didn’t see VP VP PP, and used VP V NP instead.
ROOT S VP VP PP NP Papa V ateS NP VP VP V NP N caviar P withNP Det N PP P NP N spoon Det theNP NP PP Det a
0 Papa 1 ate 2 the 3 caviar 4 with 5 a 6 spoon 7
“goal stack”
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600.465 - Intro to NLP - J. Eisner 7
First Try: Recursive Descent
1 VP . V NP 1 after dot = nonterminal, so recursively look for it (“predict”) 1 V . ate 1 after dot = terminal, so look for it in the input (“scan”) 1 V ate . 2 after dot = nothing, so parent’s subgoal is completed (“attach”)
1 VP V . NP 2 predict (next subgoal) 2 NP . ... 2 do some more parsing and eventually ... 2 NP ... . 7 we complete the parent’s 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 ateS NP VP VP VP PP N caviar P withNP Det N PP P NP N spoon Det theNP NP PP Det a
0 Papa 1 ate 2 the 3 caviar 4 with 5 a 6 spoon 7
0 ROOT . S 0 0 S . NP VP 0
0 NP . Papa 0 0 NP Papa . 1
0 S NP . VP 1 after dot = nonterminal, so recursively look for it (“predict”)
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600.465 - Intro to NLP - J. Eisner 8
First Try: Recursive Descent
0 ROOT . S 0 0 S . NP VP 0
0 NP . Papa 0 0 NP Papa . 1
0 S NP . VP 1 1 VP . V NP 1
1 V . ate 1 1 V ate . 2
1 VP V . NP 2 2 NP . ... 2 2 NP ... . 7
1 VP V NP . 7 0 S NP VP . 7
ROOT S VP V NP NP Papa V ateS NP VP VP VP PP N caviar P withNP Det N PP P NP N spoon Det theNP NP PP Det a
But how about the other parse?
must backtrack to try predicting a different VP rule here instead
0 Papa 1 ate 2 the 3 caviar 4 with 5 a 6 spoon 7
implement by function calls:S() calls NP() and VP(), which recurse
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600.465 - Intro to NLP - J. Eisner 9
First Try: Recursive Descent
1 VP . V NP 1 1 V . ate 1 1 V ate . 2
1 VP V . NP 2 2 NP . ... 2 do some more parsing and eventually ... 2 NP ... . 4 ... the correct NP is from 2 to 4 this time
(but might we find the one from 2 to 7 instead?)
ROOT S VP V NP NP Papa V ateS NP VP VP VP PP N caviar P withNP Det N PP P NP N spoon Det theNP NP PP Det a
we’d better backtrack here too! (why?)
0 Papa 1 ate 2 the 3 caviar 4 with 5 a 6 spoon 7
0 ROOT . S 0 0 S . NP VP 0
0 NP . Papa 0 0 NP Papa . 1
0 S NP . VP 1 1 VP . VP PP 1
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600.465 - Intro to NLP - J. Eisner 10
First Try: Recursive Descent
1 VP . VP PP 1 1 VP . VP PP 1 1 VP . VP PP 1 oops, stack overflowed
no fix after all – must transform grammar to eliminate
left-recursive rules
ROOT S VP V NP NP Papa V ateS NP VP VP VP PP N caviar P withNP Det N PP P NP N spoon Det theNP NP PP Det a
0 Papa 1 ate 2 the 3 caviar 4 with 5 a 6 spoon 7
0 ROOT . S 0 0 S . NP VP 0
0 NP . Papa 0 0 NP Papa . 1
0 S NP . VP 1 1 VP . VP PP 1
1 VP . VP PP 1
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600.465 - Intro to NLP - J. Eisner 11
Use a Parse Table (= “Chart”) Earley’s algorithm resembles recursive descent, but solves the left-recursion
problem. No recursive function calls. Use a parse table as we did in CKY, so we can look up anything we’ve discovered
so far. “Dynamic programming.”
Entries in column 5 look like (3, S NP . VP) (but we’ll omit the etc. to save space) Built while processing word 5 Means that the input substring from 3 to 5
matches the initial NP portion of a S NP VP rule Dot shows how much we’ve matched as of column 5 Perfectly fine to have entries like (3, S is it . true that S)
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600.465 - Intro to NLP - J. Eisner 12
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: Doesn’t mean we’ll 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 we’ll be able to attach the S to something. And when that something is complete, it too will have a customer to
its left … just as in recursive descent! In short, a top-down (i.e., goal-directed) parser: it chooses to start
building a constituent not because of the input but because that’s what the left context needs. In the spoon, won’t build spoon as a verb because there’s no way to use a verb there.
So any hypothesis in column 5 could get used in the correct parse, if words 1-5 are continued in just the right way by words 6-n.
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600.465 - Intro to NLP - J. Eisner 13
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 hypothesesold hypotheses
Process a hypothesis according to what follows the dot – just as in recursive descent: If a word, scan input and see if it matches If a nonterminal, predict ways to match it
(we’ll predict blindly, but could reduce # of predictions by looking ahead k symbols in the input and only making predictions 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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600.465 - Intro to NLP - J. Eisner 14
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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600.465 - Intro to NLP - J. Eisner 15
(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 jbludger
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600.465 - Intro to NLP - J. Eisner 16
Scan
(i, A B C . D E)
column j
D
j jbludger
(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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600.465 - Intro to NLP - J. Eisner 17
Attach
D
j k
(i, A B C . D E)
column j column k(j, D bludger .)
…
current hypothesis (complete)
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600.465 - Intro to NLP - J. Eisner 18
Attach
D
j kB 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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600.465 - Intro to NLP - J. Eisner 19
Our Usual Example Grammar
ROOT SS NP VP NP PapaNP Det N N caviarNP NP PP N spoonVP VP PP V ateVP V NP P withPP P NP Det the
Det a
0 Papa 1 ate 2 the 3 caviar 4 with 5 a 6 spoon 7
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0
0 ROOT . Sinitialize
Remember this stands for (0, ROOT . S)
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0
0 ROOT . S
0 S . NP VPpredict 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 N
0 NP . NP PP
0 NP . Papa
predict the kind of NP we are looking for(actually we’ll 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 N
0 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 N
0 NP . NP PP
0 NP . Papa
0 Det . the
0 Det . a
predict the kind of NP we’re looking for but we were already looking for these sodon’t add duplicate goals! Note that this happenedwhen 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 N
0 NP . NP PP
0 NP . Papa
0 Det . the
0 Det . a
scan: the desired word is in the input!
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0 Papa 1
0 ROOT . S 0 NP Papa .
0 S . NP VP
0 NP . Det N
0 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 N
0 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 . PP
0 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 . PP
0 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 . PP
0 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 . PP
0 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 . PP
0 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 . PP
0 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 . PP
0 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 . PP
0 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 . PP
0 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 N
0 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 N
0 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 N
0 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 N
0 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 N
0 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 N
0 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
0 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 . caviar
0 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 . caviar
0 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 . caviar
0 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 . caviar
0 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 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
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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0 Papa 1 ate 2 the 3 caviar 4 with 5 a 6
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 4 P with . 5 Det a .
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 a 6
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 4 P with . 5 Det a .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP 5 NP Det . N
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 a 6
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 4 P with . 5 Det a .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP 5 NP Det . N
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 5 NP . Det N 6 N . caviar
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP . NP PP 6 N . spoon
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 a 6
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 4 P with . 5 Det a .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP 5 NP Det . N
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 5 NP . Det N 6 N . caviar
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP . NP PP 6 N . spoon
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 a 6 spoon 7
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 4 P with . 5 Det a . 6 N spoon .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP 5 NP Det . N
0 NP . Det N 0 NP NP . PP 2 NP . Det N 3 N . caviar 1 VP V NP . 5 NP . Det N 6 N . caviar
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP . NP PP 6 N . spoon
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 a 6 spoon 7
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 4 P with . 5 Det a . 6 N spoon .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP 5 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 . 5 NP . Det N 6 N . caviar
0 NP . NP PP 1 VP . V NP 2 NP . NP PP 3 N . spoon 2 NP NP . PP 5 NP . NP PP 6 N . spoon
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 a 6 spoon 7
0 ROOT . S 0 NP Papa . 1 V ate . 2 Det the . 3 N caviar . 4 P with . 5 Det a . 6 N spoon .
0 S . NP VP 0 S NP . VP 1 VP V . NP 2 NP Det . N 2 NP Det N . 4 PP P . NP 5 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 . 5 NP . Det N 6 N . caviar 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 6 N . spoon 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 a spoon 7
0 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 7
0 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 7
0 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 7
0 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 7
0 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 7
0 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 7
0 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 7
0 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 7
0 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 7
0 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 7
0 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 7
0 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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600.465 - Intro to NLP - J. Eisner 81
Left Recursion Kills Pure Top-Down Parsing …
VP
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600.465 - Intro to NLP - J. Eisner 82
Left Recursion Kills Pure Top-Down Parsing …
VP
VP PP
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600.465 - Intro to NLP - J. Eisner 83
Left Recursion Kills Pure Top-Down Parsing …
VP PP
VP
VP PP
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600.465 - Intro to NLP - J. Eisner 84
Left Recursion Kills Pure Top-Down Parsing …
VP PP
VP
VP PP
VP PP
makes new hypothesesad infinitum before we’veseen the PPs at all
hypotheses try to predictin advance how many PP’s will arrive in input
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600.465 - Intro to NLP - J. Eisner 85
… but Earley’s Alg is Okay!VP
PPVP
1 VP . VP PP
(in column 1)
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600.465 - Intro to NLP - J. Eisner 86
… but Earley’s Alg is Okay!
VP
V NP
1 VP V NP .
ate the caviar
VP
PPVP
1 VP . VP PP
(in column 1)
(in column 4)
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600.465 - Intro to NLP - J. Eisner 87
… but Earley’s Alg is Okay!
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)
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600.465 - Intro to NLP - J. Eisner 88
… but Earley’s Alg is Okay!
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)
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600.465 - Intro to NLP - J. Eisner 89
… but Earley’s Alg is Okay!
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)
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600.465 - Intro to NLP - J. Eisner 90
… but Earley’s Alg is Okay!
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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600.465 - Intro to NLP - J. Eisner 91
… but Earley’s Alg is Okay!
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(in column 1)
(in column 10)
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600.465 - Intro to NLP - J. Eisner 92
… but Earley’s Alg is Okay!
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)
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600.465 - Intro to NLP - J. Eisner 93
… but Earley’s Alg is Okay!
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
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0 Papa 1 ate 2 the 3 caviar 4 with a spoon 7
0 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 .
completed a VP in col 4col 1 lets us use it in a VP PP structure
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0 Papa 1 ate 2 the 3 caviar 4 with a spoon 7
0 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 .
completed that VP = VP PP in col 7col 1 would let us use it in a VP PP structurecan reuse col 1 as often as we need
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600.465 - Intro to NLP - J. Eisner 96
What’s the Complexity?