Natural Language Processing Info 159/259 Lecture 17: Dependency - PowerPoint PPT Presentation

☞ flight action arc stack iobj(book, me) LeftArc(label): assert relation between head at stack 1 (morning) and dependent at morning stack 2 (the) : remove stack 2 (the) the RightArc(label): assert relation between head at stack 2 (the) and dependent book at stack 1 (morning); remove stack 1 (morning) ∅ Shift: Remove word from front of input buffer (flight) and push it onto stack

☞ action arc stack iobj(book, me) LeftArc(label): assert relation flight between head at stack 1 (morning) and dependent at morning stack 2 (the) : remove stack 2 (the) the RightArc(label): assert relation between head at stack 2 (the) and dependent book at stack 1 (morning); remove stack 1 (morning) ∅ Shift: Remove word from front of input buffer (flight) and push it onto stack

action arc stack iobj(book, me) LeftArc(label): assert relation flight between head at stack 1 nmod(flight, morning) (flight) and dependent at morning stack 2 (morning) : remove stack 2 (morning) the RightArc(label): assert relation between head at stack 2 (morning) and book dependent at stack 1 (flight); remove stack 1 (flight) ∅ Shift: Remove word from front of input buffer and push it onto stack

☞ action arc stack iobj(book, me) LeftArc(label): assert relation flight between head at stack 1 nmod(flight, morning) (flight) and dependent at morning stack 2 (morning) : remove stack 2 (morning) the RightArc(label): assert relation between head at stack 2 (morning) and book dependent at stack 1 (flight); remove stack 1 (flight) ∅ Shift: Remove word from front of input buffer and push it onto stack

☞ action arc stack iobj(book, me) LeftArc(label): assert relation flight between head at stack 1 nmod(flight, morning) (flight) and dependent at stack 2 (morning) : remove stack 2 (morning) the RightArc(label): assert relation between head at stack 2 (morning) and book dependent at stack 1 (flight); remove stack 1 (flight) ∅ Shift: Remove word from front of input buffer and push it onto stack

action arc stack iobj(book, me) LeftArc(label): assert relation flight between head at stack 1 nmod(flight, morning) (flight) and dependent at stack 2 (the) : remove stack 2 (the) the RightArc(label): assert relation between head at stack 2 (the) and dependent book at stack 1 (flight); remove stack 1 (flight) ∅ Shift: Remove word from front of input buffer and push it onto stack

☞ action arc stack iobj(book, me) LeftArc(label): assert relation flight between head at stack 1 nmod(flight, morning) (flight) and dependent at stack 2 (the) : remove stack 2 (the) the RightArc(label): assert relation between head at stack 2 (the) and dependent book at stack 1 (flight); remove stack 1 (flight) ∅ Shift: Remove word from front of input buffer and push it onto stack

☞ action arc stack iobj(book, me) LeftArc(label): assert relation flight between head at stack 1 nmod(flight, morning) (flight) and dependent at stack 2 (the) : remove stack 2 (the) det(flight, the) the RightArc(label): assert relation between head at stack 2 (the) and dependent book at stack 1 (flight); remove stack 1 (flight) ∅ Shift: Remove word from front of input buffer and push it onto stack

☞ action arc stack iobj(book, me) LeftArc(label): assert relation flight between head at stack 1 nmod(flight, morning) (flight) and dependent at stack 2 (the) : remove stack 2 (the) det(flight, the) RightArc(label): assert relation between head at stack 2 (the) and dependent book at stack 1 (flight); remove stack 1 (flight) ∅ Shift: Remove word from front of input buffer and push it onto stack

action arc stack iobj(book, me) LeftArc(label): assert relation flight between head at stack 1 nmod(flight, morning) (flight) and dependent at stack 2 (book) : remove stack 2 (book) det(flight, the) RightArc(label): assert relation between head at stack 2 (book) and book dependent at stack 1 (flight); remove stack 1 (flight) ∅ Shift: Remove word from front of input buffer and push it onto stack

☞ action arc stack iobj(book, me) LeftArc(label): assert relation flight between head at stack 1 nmod(flight, morning) (flight) and dependent at stack 2 (book) : remove stack 2 (book) det(flight, the) RightArc(label): assert relation between head at stack 2 (book) and book dependent at stack 1 (flight); remove stack 1 (flight) ∅ Shift: Remove word from front of input buffer and push it onto stack

☞ action arc stack iobj(book, me) LeftArc(label): assert relation flight between head at stack 1 nmod(flight, morning) (flight) and dependent at stack 2 (book) : remove stack 2 (book) det(flight, the) RightArc(label): assert obj(book, flight) relation between head at stack 2 (book) and book dependent at stack 1 (flight); remove stack 1 (flight) ∅ Shift: Remove word from front of input buffer and push it onto stack

☞ action arc stack iobj(book, me) LeftArc(label): assert relation between head at stack 1 nmod(flight, morning) (flight) and dependent at stack 2 (book) : remove stack 2 (book) det(flight, the) RightArc(label): assert obj(book, flight) relation between head at stack 2 (book) and book dependent at stack 1 (flight); remove stack 1 (flight) ∅ Shift: Remove word from front of input buffer and push it onto stack

action arc stack iobj(book, me) LeftArc(label): assert relation between head at stack 1 nmod(flight, morning) (book) and dependent at stack 2 ( ∅ ) : remove stack 2 ( ∅ ) det(flight, the) RightArc(label): assert relation between head at obj(book, flight) stack 2 ( ∅ ) and dependent at book stack 1 (book); remove stack 1 (book) ∅ Shift: Remove word from front of input buffer and push it onto stack

☞ action arc stack iobj(book, me) LeftArc(label): assert relation between head at stack 1 nmod(flight, morning) (book) and dependent at stack 2 ( ∅ ) : remove stack 2 ( ∅ ) det(flight, the) RightArc(label): assert relation between head at obj(book, flight) stack 2 ( ∅ ) and dependent at book stack 1 (book); remove stack 1 (book) ∅ Shift: Remove word from front of input buffer and push it onto stack

☞ action arc stack iobj(book, me) LeftArc(label): assert relation between head at stack 1 nmod(flight, morning) (book) and dependent at stack 2 ( ∅ ) : remove stack 2 ( ∅ ) det(flight, the) RightArc(label): assert relation between head at obj(book, flight) stack 2 ( ∅ ) and dependent at book stack 1 (book); remove stack 1 root( ∅ , book) (book) ∅ Shift: Remove word from front of input buffer and push it onto stack

☞ action arc stack iobj(book, me) LeftArc(label): assert relation between head at stack 1 nmod(flight, morning) (book) and dependent at stack 2 ( ∅ ) : remove stack 2 ( ∅ ) det(flight, the) RightArc(label): assert relation between head at obj(book, flight) stack 2 ( ∅ ) and dependent at stack 1 (book); remove stack 1 root( ∅ , book) (book) ∅ Shift: Remove word from front of input buffer and push it onto stack

☞ This is our parse action arc stack iobj(book, me) LeftArc(label): assert relation between head at stack 1 nmod(flight, morning) (book) and dependent at stack 2 ( ∅ ) : remove stack 2 ( ∅ ) det(flight, the) RightArc(label): assert relation between head at obj(book, flight) stack 2 ( ∅ ) and dependent at stack 1 (book); remove stack 1 root( ∅ , book) (book) ∅ Shift: Remove word from front of input buffer and push it onto stack

This is our parse arc iobj(book, me) nmod(flight, morning) det(flight, the) obj(book, flight) root( ∅ , book)

Let’s go back to this earlier the morning flight configuration action arc stack LeftArc(label): assert relation between head at stack 1 (me) and dependent at stack 2 (book) : remove stack 2 (book) RightArc(label): assert me relation between head at stack 2 (book) and book dependent at stack 1 (me); remove stack 1 (me) ∅ Shift: Remove word from front of input buffer (the) and push it onto stack

Output space 𝓩 = Shift LeftArc(nsubj) RightArc(nsubj) • This is a multi class classification problem: LeftArc(det) given the current configuration — i.e., the RightArc(det) elements in the stack, the words in the buffer, LeftArc(obj) and the arcs created so far, what’s the best RightArc(obj) transition? …

stack me book buffer the morning flight arc

Features are scoped over the stack, buffer, and arcs created so far stack me book buffer the morning flight arc

Features are scoped over the stack, feature example buffer, and arcs created so far stack me book buffer the morning flight arc

Features are scoped over the stack, feature example buffer, and arcs created so far stack 1 = me 1 stack me book buffer the morning flight arc

Features are scoped over the stack, feature example buffer, and arcs created so far stack 1 = me 1 stack 2 = book 1 stack me book buffer the morning flight arc

Features are scoped over the stack, feature example buffer, and arcs created so far stack 1 = me 1 stack 2 = book 1 stack me stack 1 POS = PRP 1 book buffer the morning flight arc

Features are scoped over the stack, feature example buffer, and arcs created so far stack 1 = me 1 stack 2 = book 1 stack me stack 1 POS = PRP 1 book buffer 1 = the 1 buffer the morning flight arc

Features are scoped over the stack, feature example buffer, and arcs created so far stack 1 = me 1 stack 2 = book 1 stack me stack 1 POS = PRP 1 book buffer 1 = the 1 buffer 2 = morning 1 buffer the morning flight arc

Features are scoped over the stack, feature example buffer, and arcs created so far stack 1 = me 1 stack 2 = book 1 stack me stack 1 POS = PRP 1 book buffer 1 = the 1 buffer 2 = morning 1 buffer buffer 1 = today 0 the morning flight arc

Features are scoped over the stack, feature example buffer, and arcs created so far stack 1 = me 1 stack 2 = book 1 stack me stack 1 POS = PRP 1 book buffer 1 = the 1 buffer 2 = morning 1 buffer buffer 1 = today 0 the morning flight buffer 1 POS = RB 0 arc

Features are scoped over the stack, feature example buffer, and arcs created so far stack 1 = me 1 stack 2 = book 1 stack me stack 1 POS = PRP 1 book buffer 1 = the 1 buffer 2 = morning 1 buffer buffer 1 = today 0 the morning flight buffer 1 POS = RB 0 stack 1 = me AND 1 stack 2 = book arc

Features are scoped over the stack, feature example buffer, and arcs created so far stack 1 = me 1 stack 2 = book 1 stack me stack 1 POS = PRP 1 book buffer 1 = the 1 buffer 2 = morning 1 buffer buffer 1 = today 0 the morning flight buffer 1 POS = RB 0 stack 1 = me AND 1 stack 2 = book arc stack 1 = PRP AND 1 stack 2 = VB

Features are scoped over the stack, feature example buffer, and arcs created so far stack 1 = me 1 stack 2 = book 1 stack me stack 1 POS = PRP 1 book buffer 1 = the 1 buffer 2 = morning 1 buffer buffer 1 = today 0 the morning flight buffer 1 POS = RB 0 stack 1 = me AND 1 stack 2 = book arc stack 1 = PRP AND 1 stack 2 = VB iobj(book,*) in arcs 0

feature example β stack 1 = me 1 0.7 stack 2 = 1 1.3 book stack 1 POS = 1 6.4 PRP Use any multiclass classification buffer 1 = the 1 -1.3 model buffer 2 = • Logistic regression 1 -0.07 morning • SVM buffer 1 = • NB 0 0.52 today • Neural network buffer 1 POS = 0 -2.1 RB stack 1 = me 1 0 AND stack 2 = book stack 1 = PRP 1 -0.1 AND stack 2 = VB iobj(book,*) 0 3.2 in arcs

Training We’re training to predict the parser action (Shift, RightArc, LeftArc) given the featurized configuration Configuration features Label <stack1 = me, 1>, <stack2 = book, 1>, <stack1 POS = PRP , Shift 1>, <bu ff er1 = the, 1>, <stack1 = me, 0>, <stack2 = book, 0>, <stack1 POS = PRP , RightArc(det) 0>, <bu ff er1 = the, 0>, <stack1 = me, 0>, <stack2 = book, 1>, <stack1 POS = PRP , RightArc(nsubj) 0>, <bu ff er1 = the, 0>,

Training data Our training data comes from treebanks (native dependency syntax or converted to dependency trees).

Oracle • An algorithm for converting a gold-standard dependency tree into a series of actions a transition- based parser should follow to yield the tree. Configuration Label features <stack1 = me, 1>, Shift → <stack2 = book, 1>, <stack1 = me, 0>, RightArc(det) <stack2 = book, 0>, <stack1 = me, 0>, RightArc(nsu <stack2 = book, 1>, bj)

This is our parse arc iobj(book, me) nmod(flight, morning) det(flight, the) obj(book, flight) root( ∅ , book)

book me the morning flight ∅ action gold tree stack iobj(book, me) nmod(flight, morning) det(flight, the) obj(book, flight) root( ∅ , book)

book me the morning flight ∅ action gold tree stack iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been generated. Remove stack 1 root( ∅ , book) Else shift: Remove word from front of input buffer and push it onto stack

book me the morning flight action gold tree stack iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

book me the morning flight action gold tree stack iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

me the morning flight action gold tree stack iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

root( ∅ , book) exists but book me the morning flight has dependents in gold tree! action gold tree stack iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

me the morning flight action gold tree stack iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

the morning flight action gold tree stack iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists me in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

iobj(book, me) exists and me the morning flight has no dependents in gold tree action gold tree stack iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists me in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

the morning flight action gold tree stack ✅ iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists me in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

the morning flight action gold tree stack ✅ iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

morning flight action gold tree stack ✅ iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists the in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

morning flight action gold tree stack ✅ iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists the in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

flight action gold tree stack ✅ iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . morning Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists the in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

flight action gold tree stack ✅ iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . morning Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists the in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

action gold tree stack ✅ iobj(book, me) flight Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . morning Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists the in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

action gold tree stack ✅ iobj(book, me) flight Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . morning Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists the in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

nmod(flight,morning) action gold tree stack ✅ iobj(book, me) flight Choose LeftArc(label) if label(stack 1, stack 2 ) exists in nmod(flight, morning) gold tree. Remove stack 2 . morning Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists the in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

nmod(flight,morning) action gold tree stack ✅ iobj(book, me) flight Choose LeftArc(label) if label(stack 1, stack 2 ) exists in ✅ nmod(flight, morning) gold tree. Remove stack 2 . morning Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists the in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

nmod(flight,morning) action gold tree stack ✅ iobj(book, me) flight Choose LeftArc(label) if label(stack 1, stack 2 ) exists in ✅ nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists the in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

action gold tree stack ✅ iobj(book, me) flight Choose LeftArc(label) if label(stack 1, stack 2 ) exists in ✅ nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists the in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

det(flight,the) action gold tree stack ✅ iobj(book, me) flight Choose LeftArc(label) if label(stack 1, stack 2 ) exists in ✅ nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) det(flight, the) if label(stack 2, stack 1 ) exists the in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

det(flight,the) action gold tree stack ✅ iobj(book, me) flight Choose LeftArc(label) if label(stack 1, stack 2 ) exists in ✅ nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) ✅ det(flight, the) if label(stack 2, stack 1 ) exists the in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

det(flight,the) action gold tree stack ✅ iobj(book, me) flight Choose LeftArc(label) if label(stack 1, stack 2 ) exists in ✅ nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) ✅ det(flight, the) if label(stack 2, stack 1 ) exists in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

action gold tree stack ✅ iobj(book, me) flight Choose LeftArc(label) if label(stack 1, stack 2 ) exists in ✅ nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) ✅ det(flight, the) if label(stack 2, stack 1 ) exists in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

obj(book,flight) action gold tree stack ✅ iobj(book, me) flight Choose LeftArc(label) if label(stack 1, stack 2 ) exists in ✅ nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) ✅ det(flight, the) if label(stack 2, stack 1 ) exists in gold tree and all arcs obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

obj(book,flight) action gold tree stack ✅ iobj(book, me) flight Choose LeftArc(label) if label(stack 1, stack 2 ) exists in ✅ nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) ✅ det(flight, the) if label(stack 2, stack 1 ) exists in gold tree and all arcs ✅ obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

obj(book,flight) action gold tree stack ✅ iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in ✅ nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) ✅ det(flight, the) if label(stack 2, stack 1 ) exists in gold tree and all arcs ✅ obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

action gold tree stack ✅ iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in ✅ nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) ✅ det(flight, the) if label(stack 2, stack 1 ) exists in gold tree and all arcs ✅ obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

root( ∅ , book) and book has no more dependents we haven’t seen action gold tree stack ✅ iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in ✅ nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) ✅ det(flight, the) if label(stack 2, stack 1 ) exists in gold tree and all arcs ✅ obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack

root( ∅ , book) and book has no more dependents we haven’t seen action gold tree stack ✅ iobj(book, me) Choose LeftArc(label) if label(stack 1, stack 2 ) exists in ✅ nmod(flight, morning) gold tree. Remove stack 2 . Else choose RightArc(label) ✅ det(flight, the) if label(stack 2, stack 1 ) exists in gold tree and all arcs ✅ obj(book, flight) label(stack 1 , *). have been book generated. Remove stack 1 ✅ root( ∅ , book) Else shift: Remove word ∅ from front of input buffer and push it onto stack