Tree Transducers in Machine Translation
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1 Tree Transducers in Machine Translation Andreas Maletti Universitat Rovira i Virgili Tarragona, pain andreas.maletti@urv.cat Jena August 23, 2010 Tree Transducers in MT A. Maletti 1
2 Machine translation Applications Technical manuals Example (An mp3 player) The synchronous manifestation of lyrics is a procedure for can roadcasting the music, waiting the mp3 file at the same time showing the lyrics. With the this kind method that the euipments that synchronous function of support up roadcast to make use of document create setup, you can pass the LCD window way the check at the document contents that roadcast. That procedure returns offerings to have to modify, and delete, and stick top, keep etc. edit function. Tree Transducers in MT A. Maletti 2
3 Machine translation Applications Technical manuals Example (An mp3 player) The synchronous manifestation of lyrics is a procedure for can roadcasting the music, waiting the mp3 file at the same time showing the lyrics. With the this kind method that the euipments that synchronous function of support up roadcast to make use of document create setup, you can pass the LCD window way the check at the document contents that roadcast. That procedure returns offerings to have to modify, and delete, and stick top, keep etc. edit function. Tree Transducers in MT A. Maletti 2
4 Machine translation Applications Technical manuals Example (An mp3 player) The synchronous manifestation of lyrics is a procedure for can roadcasting the music, waiting the mp3 file at the same time showing the lyrics. With the this kind method that the euipments that synchronous function of support up roadcast to make use of document create setup, you can pass the LCD window way the check at the document contents that roadcast. That procedure returns offerings to have to modify, and delete, and stick top, keep etc. edit function. Tree Transducers in MT A. Maletti 2
5 Machine translation Applications Technical manuals TripAdvisor R Example (Hotel Uppsala, weden) Wir hatten die Zimmer eingestuft wird als uperior weil sie renoviert wurde im letzten Jahr oder zwei. Unsere Zimmer hatten Parkettoden und waren sehr geräumig. Man musste allerdings nicht musste seitwärts ewegen. Tree Transducers in MT A. Maletti 2
6 Machine translation Applications Technical manuals TripAdvisor R Example (Hotel Uppsala, weden) Nos alojamos en haitaciones clasificado como superior porue se lo haían renovado en el año pasado o dos. Nuestras haitaciones tenían suelos de madera y eran espaciosas. No te tenías ue caminar arria para movernos por allí. Tree Transducers in MT A. Maletti 2
7 Machine translation Applications Technical manuals TripAdvisor R Example (Hotel Uppsala, weden) Wir hatten die Zimmer eingestuft wird als uperior weil sie renoviert wurde im letzten Jahr oder zwei. Unsere Zimmer hatten Parkettoden und waren sehr geräumig. Man musste allerdings nicht musste seitwärts ewegen. We stayed in rooms classified as superior ecause they had een renovated in the last year or two. Our rooms had wood floors and were roomy. You didn t have to walk sideways to move around. Tree Transducers in MT A. Maletti 2
8 Machine translation Applications Technical manuals TripAdvisor R Military Example (JONE, HEN, HERZOG 2009) oldier: Okay, what is your name? Local: Adul. oldier: And your last name? Local: Al Farran. Tree Transducers in MT A. Maletti 2
9 Machine translation Applications Technical manuals TripAdvisor R Military Example (JONE, HEN, HERZOG 2009) oldier: Okay, what is your name? Local: Adul. oldier: And your last name? Local: Al Farran. peech-to-text machine translation oldier: Local: Okay, what s your name? milk a mechanic and I am here I mean yes Tree Transducers in MT A. Maletti 2
10 Machine translation Applications Technical manuals TripAdvisor R Military Example (JONE, HEN, HERZOG 2009) oldier: Okay, what is your name? Local: Adul. oldier: And your last name? Local: Al Farran. peech-to-text machine translation oldier: Local: oldier: Local: Okay, what s your name? milk a mechanic and I am here I mean yes What is your last name? every two weeks my son s name is ismail Tree Transducers in MT A. Maletti 2
11 Machine translation Applications Technical manuals TripAdvisor R Military MDN, Knowledge Base... Tree Transducers in MT A. Maletti 2
12 Machine translation (cont d) ystems GOOGLE translate BING translator LANGUAGE WEAVER + DL... translate.google.com Tree Transducers in MT A. Maletti 3
13 Machine translation (cont d) ystems GOOGLE translate BING translator LANGUAGE WEAVER + DL... translate.google.com Try them! Tree Transducers in MT A. Maletti 3
14 Machine translation (cont d) History 1 Dark age (60s 90s) rule-ased systems (e.g., YTRAN) CHOMKYAN approach perfect translation, poor coverage 2 Reformation (1991 present) word-ased, phrase-ased, syntax-ased systems statistical approach cheap, automatically trained 3 Potential future semantics-ased systems (e.g., FRAMENET) semi-supervised, statistical approach asic understanding of translated text Tree Transducers in MT A. Maletti 4
15 Machine translation (cont d) History 1 Dark age (60s 90s) rule-ased systems (e.g., YTRAN) CHOMKYAN approach perfect translation, poor coverage 2 Reformation (1991 present) word-ased, phrase-ased, syntax-ased systems statistical approach cheap, automatically trained 3 Potential future semantics-ased systems (e.g., FRAMENET) semi-supervised, statistical approach asic understanding of translated text Tree Transducers in MT A. Maletti 4
16 Machine translation (cont d) History 1 Dark age (60s 90s) rule-ased systems (e.g., YTRAN) CHOMKYAN approach perfect translation, poor coverage 2 Reformation (1991 present) word-ased, phrase-ased, syntax-ased systems statistical approach cheap, automatically trained 3 Potential future semantics-ased systems (e.g., FRAMENET) semi-supervised, statistical approach asic understanding of translated text Tree Transducers in MT A. Maletti 4
17 Machine translation (cont d) chema Input Machine translation system Language model Output Tree Transducers in MT A. Maletti 5
18 Machine translation (cont d) chema Input Machine translation system Language model Output Tree Transducers in MT A. Maletti 5
19 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: And then the matter was decided, and everything was put in place Output: Tree Transducers in MT A. Maletti 6
20 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: then the matter was decided, and everything was put in place Output: Tree Transducers in MT A. Maletti 6
21 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: the matter was decided, and everything was put in place Output: Tree Transducers in MT A. Maletti 6
22 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: the matter was decided, and everything was put in place Output: f Tree Transducers in MT A. Maletti 6
23 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: the matter was decided, and everything was put in place Output: f kan Tree Transducers in MT A. Maletti 6
24 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: the matter was decided, and everything was put in place Output: f kan Tree Transducers in MT A. Maletti 6
25 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: the matter was decided, and everything was put in place Output: f kan Tree Transducers in MT A. Maletti 6
26 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: the matter was decided, and everything was put in place Output: f kan Tree Transducers in MT A. Maletti 6
27 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: the matter, and everything was put in place Output: f kan An tm AlHsm Tree Transducers in MT A. Maletti 6
28 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: the matter and everything was put in place Output: f kan An tm AlHsm Tree Transducers in MT A. Maletti 6
29 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: the matter everything was put in place Output: f kan An tm AlHsm w Tree Transducers in MT A. Maletti 6
30 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: the matter was put in place Output: f kan An tm AlHsm w Tree Transducers in MT A. Maletti 6
31 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: the matter was put in place Output: f kan An tm AlHsm w Tree Transducers in MT A. Maletti 6
32 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: the matter in place Output: f kan An tm AlHsm w wdet Tree Transducers in MT A. Maletti 6
33 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: in place Output: f kan An tm AlHsm w wdet Almwr Tree Transducers in MT A. Maletti 6
34 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: place Output: f kan An tm AlHsm w wdet Almwr fy Tree Transducers in MT A. Maletti 6
35 Word-ased system (FT) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: Output: f kan An tm AlHsm w wdet Almwr fy na ha Tree Transducers in MT A. Maletti 6
36 Phrase-ased machine translation chema Input Machine translation system Language model Output Phrase-ased systems Input egmenter Machine translation system Language model Output Tree Transducers in MT A. Maletti 7
37 Phrase-ased machine translation chema Input Machine translation system Language model Output Phrase-ased systems Input egmenter Machine translation system Language model Output Tree Transducers in MT A. Maletti 7
38 Phrase-ased system (FT+Perm) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: And then the matter was decided, and everything was put in place Output: Tree Transducers in MT A. Maletti 8
39 Phrase-ased system (FT+Perm) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: And then 1 the matter 5 was decided 2, and everything 3 was put 4 in place 6 Output: Tree Transducers in MT A. Maletti 8
40 Phrase-ased system (FT+Perm) And then the matter was decided, and everything was put in place f kan An tm AlHsm w wdet Almwr fy na ha Derivation Input: And then 1 the matter 5 was decided 2, and everything 3 was put 4 in place 6 Output: f kan 1 An tm AlHsm 2 w 3 wdet 4 Almwr 5 fy na ha 6 Tree Transducers in MT A. Maletti 8
41 Machine translation (cont d) Phrase-ased systems Input egmenter Machine translation system Language model Output yntax-ased systems Input Parser Machine translation system Language model Output Tree Transducers in MT A. Maletti 9
42 Machine translation (cont d) Phrase-ased systems Input egmenter Machine translation system Language model Output yntax-ased systems Input Parser Machine translation system Language model Output Tree Transducers in MT A. Maletti 9
43 Parser CC CC AD -BJ-9 and -BJ-1 And RB DT NN VBD NN VBD then the matter was VBN -9 everything was VBN -1 PP decided, put * IN in NN place And then the matter was decided, and everything was put in place (thanks to KEVIN KNIGHT for the data) Tree Transducers in MT A. Maletti 10
44 CC And AD RB then -BJ-9 DT the NN matter VBD was VBN decided -9, CC and -BJ-1 NN everything VBD was VBN put -1 * PP IN in NN place CONJ f PV kan -BJ * BAR UB An PV tm -BJ DET-NN AlHsm CONJ w PV wdet -BJ1 DET-NN Almwr -OBJ1 * PP PREP fy NN na PO ha Tree Transducers in MT A. Maletti 11
45 -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N eria rya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ Tree Transducers in MT A. Maletti 12
46 Contents 1 Machine Translation 2 Extended Top-down Tree Transducers 3 Multi Bottom-up Tree Transducers 4 ynchronous Tree-Adjoining Grammars Tree Transducers in MT A. Maletti 13
47 Weight structure Definition Commutative semiring (C, +,, 0, 1) if (C, +, 0) and (C,, 1) commutative monoids distriutes over finite (incl. empty) sums Example BOOLEAN semiring ({0, 1}, max, min, 0, 1) emiring (R 0, +,, 0, 1) of proailities Tropical semiring (N { }, min, +,, 0) Any field, ring, etc. Most of the talk: BOOLEAN semiring Tree Transducers in MT A. Maletti 14
48 Weight structure Definition Commutative semiring (C, +,, 0, 1) if (C, +, 0) and (C,, 1) commutative monoids distriutes over finite (incl. empty) sums Example BOOLEAN semiring ({0, 1}, max, min, 0, 1) emiring (R 0, +,, 0, 1) of proailities Tropical semiring (N { }, min, +,, 0) Any field, ring, etc. Most of the talk: BOOLEAN semiring Tree Transducers in MT A. Maletti 14
49 Weight structure Definition Commutative semiring (C, +,, 0, 1) if (C, +, 0) and (C,, 1) commutative monoids distriutes over finite (incl. empty) sums Example BOOLEAN semiring ({0, 1}, max, min, 0, 1) emiring (R 0, +,, 0, 1) of proailities Tropical semiring (N { }, min, +,, 0) Any field, ring, etc. Most of the talk: BOOLEAN semiring Tree Transducers in MT A. Maletti 14
50 yntax Definition (ARNOLD, DAUCHET 1976, GRAEHL, KNIGHT 2004) Extended top-down tree transducer (XTOP) M = (Q, Σ,, I, R) with finitely many rules Σ x 1... x k (x i )... p(x j ),, p Q are states i, j {1,..., k} Tree Transducers in MT A. Maletti 15
51 yntax (cont d) Definition (ROUND 1970, THATCHER 1970) Top-down tree transducer (TOP) if all rules σ x 1... x k (x i )... p(x j ) linear if no variale occurs twice in r for all rules l r nondeleting if var(l) = var(r) for all rules l r Tree Transducers in MT A. Maletti 16
52 yntax (cont d) Definition (ROUND 1970, THATCHER 1970) Top-down tree transducer (TOP) if all rules σ x 1... x k (x i )... p(x j ) linear if no variale occurs twice in r for all rules l r nondeleting if var(l) = var(r) for all rules l r Tree Transducers in MT A. Maletti 16
53 yntax (cont d) Definition (ROUND 1970, THATCHER 1970) Top-down tree transducer (TOP) if all rules σ x 1... x k (x i )... p(x j ) linear if no variale occurs twice in r for all rules l r nondeleting if var(l) = var(r) for all rules l r Tree Transducers in MT A. Maletti 16
54 emantics Example tates {, V, } of which only is initial x 1 x 2 V x 2 x 1 x 2 V x 1 x 2 V x 1 x 1 x 2 x 2 Derivation t 1 t 2 t 3 V t 2 t 3 t 1 t 2 t 3 V t 2 t 1 t 2 t 3 V t 2 t 1 t 3 Tree Transducers in MT A. Maletti 17
55 emantics (cont d) Definition Computed transformation: τ M = {(t, u) T Σ T I : (t) u} Tree Transducers in MT A. Maletti 18
56 -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N eria rya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ Tree Transducers in MT A. Maletti 19
57 -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N eria rya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ Tree Transducers in MT A. Maletti 19
58 -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N eria rya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ Tree Transducers in MT A. Maletti 19
59 -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N eria rya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ Tree Transducers in MT A. Maletti 19
60 Rule extraction NML JJ N -BJ N Voislav VBD PP signed IN Yugoslav President for N eria x 1 VBD signed x 2 CONJ w PV -OBJ twly DET-NN AltwyE x 2 x 1 rya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP twly PP w PV -OBJ CONJ DET-NN DET-ADJ NN-PROP -BJ Tree Transducers in MT A. Maletti 20
61 Rule extraction NML JJ N -BJ N Voislav VBD PP signed IN Yugoslav President for N eria rya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ CONJ w PV -OBJ x 1 twly VBD x 2 DET-NN x 2 signed AltwyE -BJ -BJ x 1 N x 1 NN-PROP Voislav fwyslaf x 1 Tree Transducers in MT A. Maletti 20
62 Rule extraction NML JJ N -BJ N Voislav VBD PP signed IN Yugoslav President for N eria rya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ CONJ w PV -OBJ x 1 twly x 1 VBD x 2 DET-NN x 2 signed AltwyE -BJ -BJ x 1 N x 1 NN-PROP Voislav fwyslaf NML DET-NN DET-ADJ JJ N Alr}ys AlywgwslAfy Yugoslav President Tree Transducers in MT A. Maletti 20
63 ymmetry Original rule x 1 VBD signed x 2 CONJ w PV -OBJ twly DET-NN AltwyE x 2 x 1 Tree Transducers in MT A. Maletti 21
64 ymmetry Original rule Inverted rule x 1 VBD signed x 2 CONJ w PV -OBJ twly DET-NN AltwyE x 2 x 1 CONJ w PV -OBJ twly DET-NN x 2 x 1 x 1 VBD signed x 2 AltwyE Tree Transducers in MT A. Maletti 21
65 ymmetry Original rule Inverted rule x 1 VBD signed x 2 CONJ w PV -OBJ twly DET-NN AltwyE x 2 x 1 CONJ w PV -OBJ twly DET-NN x 2 x 1 x 1 VBD signed x 2 AltwyE Linear nondeleting XTT can e inverted Tree Transducers in MT A. Maletti 21
66 Preservation of regularity chematics Input Parser XTT Language model Output Parse trees est parse tree n-est parses all parses Can all e represented y regular tree language Tree Transducers in MT A. Maletti 22
67 Preservation of regularity chematics Input Parser Parse trees XTT... Parse trees est parse tree n-est parses all parses Can all e represented y regular tree language Tree Transducers in MT A. Maletti 22
68 Preservation of regularity chematics Input Parser Parse trees XTT... Parse trees est parse tree n-est parses all parses Can all e represented y regular tree language Tree Transducers in MT A. Maletti 22
69 Preservation of regularity chematics Input Parser Parse trees XTT... Parse trees est parse tree n-est parses all parses Can all e represented y regular tree language Tree Transducers in MT A. Maletti 22
70 Preservation of regularity (cont d) chematics Regular language XTT Regular language? Approach Input restriction Project to output Result Linear XTT preserve regularity Tree Transducers in MT A. Maletti 23
71 Preservation of regularity (cont d) chematics Regular language XTT Regular language? Approach Input restriction Project to output Result Linear XTT preserve regularity Tree Transducers in MT A. Maletti 23
72 Preservation of regularity (cont d) chematics Regular language XTT Regular language? Approach Input restriction Project to output Result Linear XTT preserve regularity Tree Transducers in MT A. Maletti 23
73 Composition chematics Parse trees XTT... Example (YAMADA, KNIGHT 2002) Reorder Insert words Translate words Tree Transducers in MT A. Maletti 24
74 Composition chematics Parse trees tage 1 XTT tage 2 XTT tage 3 XTT... Example (YAMADA, KNIGHT 2002) Reorder Insert words Translate words Tree Transducers in MT A. Maletti 24
75 Composition chematics Parse trees Composed XTT... Example (YAMADA, KNIGHT 2002) Reorder Insert words Translate words Tree Transducers in MT A. Maletti 24
76 Composition (cont d) Example (ARNOLD, DAUCHET 1982) σ t 1 σ δ t 2 t 3 δ t n 4 t n 3 δ t 1 t 2 σ t 3 σ σ t 4 t n 3 σ σ δ t 2 t 1 δ t 4 t 3 δ t n 2 t n 3 σ t n 2 t n 1 t n t n 2 σ t n 1 t n t n 1 t n Tree Transducers in MT A. Maletti 25
77 ummary Model \ Criterion EXPR YM PRE PRE 1 COMP Linear nondeleting TOP Linear TOP Linear TOP R General TOP General TOP R Linear nondeleting XTOP Linear XTOP Linear XTOP R General XTOP General XTOP R Tree Transducers in MT A. Maletti 26
78 ummary Model \ Criterion EXPR YM PRE PRE 1 COMP Linear nondeleting TOP Linear TOP Linear TOP R General TOP General TOP R Linear nondeleting XTOP Linear XTOP Linear XTOP R General XTOP General XTOP R Comp. closure ln-xtop composale ln-xtop?? Tree Transducers in MT A. Maletti 26
79 Implementation TIBURON [MAY, KNIGHT 2006] Implements XTOP (and tree automata; everything also weighted) Framework with command-line interface Optimized for machine translation Algorithms Application of XTOP to input tree/language Backward application of XTOP to output language Composition (for some XTOP) Example.(DT(the) N(oy)) -> (N(atefl)) Tree Transducers in MT A. Maletti 27
80 Implementation TIBURON [MAY, KNIGHT 2006] Implements XTOP (and tree automata; everything also weighted) Framework with command-line interface Optimized for machine translation Algorithms Application of XTOP to input tree/language Backward application of XTOP to output language Composition (for some XTOP) Example.(DT(the) N(oy)) -> (N(atefl)) Tree Transducers in MT A. Maletti 27
81 Implementation TIBURON [MAY, KNIGHT 2006] Implements XTOP (and tree automata; everything also weighted) Framework with command-line interface Optimized for machine translation Algorithms Application of XTOP to input tree/language Backward application of XTOP to output language Composition (for some XTOP) Example.(DT(the) N(oy)) -> (N(atefl)) Tree Transducers in MT A. Maletti 27
82 Multi Bottom-up Tree Transducers -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N eria rya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ Tree Transducers in MT A. Maletti 28
83 yntax Definition Extended multi ottom-up tree transducer (XMBOT) is M = (Q, Σ,, F, R) with finitely many rules Σ x 1... x l... p x m... x n x i... x j... x i... x j, p, Q are now ranked states F Q 1 final states Tree Transducers in MT A. Maletti 29
84 Example tates {f (1), (2) } with final state f and rules e e e x 1 a x 2 a a x 1 x 2 x 1 x 2 x 1 x 2 x 1 x 2 f σ x 1 x 2 Example (Derivation) a e Tree Transducers in MT A. Maletti 30
85 Example tates {f (1), (2) } with final state f and rules e e e x 1 a x 2 a a x 1 x 2 x 1 x 2 x 1 x 2 x 1 x 2 f σ x 1 x 2 Example (Derivation) a a e e e Tree Transducers in MT A. Maletti 30
86 Example tates {f (1), (2) } with final state f and rules e e e x 1 a x 2 a a x 1 x 2 x 1 x 2 x 1 x 2 x 1 x 2 f σ x 1 x 2 Example (Derivation) a a a e e e e e Tree Transducers in MT A. Maletti 30
87 Example tates {f (1), (2) } with final state f and rules e e e x 1 a x 2 a a x 1 x 2 x 1 x 2 x 1 x 2 x 1 x 2 f σ x 1 x 2 Example (Derivation) a a a a e e e e e e e Tree Transducers in MT A. Maletti 30
88 Example tates {f (1), (2) } with final state f and rules e e e x 1 a x 2 a a x 1 x 2 x 1 x 2 x 1 x 2 x 1 x 2 f σ x 1 x 2 Example (Derivation) a a a a a a e e e e e e e e e Tree Transducers in MT A. Maletti 30
89 Example tates {f (1), (2) } with final state f and rules e e e a x 1 x 2 a x 1 a x 2 x 1 x 2 x 1 x 2 x 1 x 2 f σ x 1 x 2 Example (Derivation) a e a e e a e e a e e a e a e f σ a e a e Tree Transducers in MT A. Maletti 30
90 emantics Definition Computed transformation: τ M = {(t, u) T Σ T F : t (u)} Tree Transducers in MT A. Maletti 31
91 emantics Definition Computed transformation: τ M = {(t, u) T Σ T F : t (u)} Example τ M = { t, σ(t, t) t T Σ } e e e x 1 a x 2 a a x 1 x 2 x 1 x 2 x 1 x 2 x 1 x 2 f σ x 1 x 2 Tree Transducers in MT A. Maletti 31
92 -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N eria rya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ Tree Transducers in MT A. Maletti 32
93 -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N eria rya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ Tree Transducers in MT A. Maletti 32
94 -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N eria rya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ Tree Transducers in MT A. Maletti 32
95 -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N eria rya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ Tree Transducers in MT A. Maletti 32
96 -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N eria rya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ Tree Transducers in MT A. Maletti 32
97 Rule extraction -BJ NML N VBD PP x 1 p x 2 x 3 CONJ w x 2 x 3 x 1 JJ N Voislav signed IN Yugoslav President for N eria AltwyE DET-NN twly w PV PREP PP -OBJ -BJ CONJ rya En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN DET-ADJ NN-PROP Tree Transducers in MT A. Maletti 33
98 Rule extraction -BJ NML N JJ Yugoslav N President Voislav VBD PP signed IN for N eria x 1 p x 2 x 3 VBD signed x 1 CONJ w PV twly x 2 x 3 x 1 p -OBJ DET-NN x 1 AltwyE DET-NN twly w PV PREP PP -OBJ -BJ CONJ rya En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN DET-ADJ NN-PROP AltwyE Tree Transducers in MT A. Maletti 33
99 One-symol normal form Definition Rule in one-symol normal form if it contains at most one symol Tree Transducers in MT A. Maletti 34
100 One-symol normal form Definition Rule in one-symol normal form if it contains at most one symol Example (ENGELFRIET, LILIN, 2009) x 1 x 2 x 1 x 2 Tree Transducers in MT A. Maletti 34
101 One-symol normal form Definition Rule in one-symol normal form if it contains at most one symol Example (ENGELFRIET, LILIN, 2009) x 1 x 2 x 1 x 2 In one-symol normal form x 1 x x 2 x 1 x 2 x 1 x 2 x 1 x 1 2 x 2 x 1 x2 Tree Transducers in MT A. Maletti 34
102 Basic properties Example (Copying translation) τ M = { t, σ(t, t) t T Σ } Conseuences XMBOT are not symmetric XMBOT do not preserve regularity ut they can e composed Tree Transducers in MT A. Maletti 35
103 Basic properties Example (Copying translation) τ M = { t, σ(t, t) t T Σ } Conseuences XMBOT are not symmetric XMBOT do not preserve regularity ut they can e composed Tree Transducers in MT A. Maletti 35
104 Basic properties Example (Copying translation) τ M = { t, σ(t, t) t T Σ } Conseuences XMBOT are not symmetric XMBOT do not preserve regularity ut they can e composed Tree Transducers in MT A. Maletti 35
105 Composition x σ σ p 1 p 2 x 1 x 2 x x 2 p 2 x 1 x 2 imple composition works in the typical cases [BAKER 1979, ENGELFRIET 1975] Tree Transducers in MT A. Maletti 36
106 Composition x σ σ p 1 p 2 x 1 x 2 x x 2 p 2 x 1 x 2 1 p 1 p α p 1 p 2 p x 2 x 1 α 1 p 2 x 1 x 2 imple composition works in the typical cases [BAKER 1979, ENGELFRIET 1975] Tree Transducers in MT A. Maletti 36
107 Composition x σ σ p 1 p 2 x 1 x 2 x x 2 p 2 x 1 x 2 p 1 p α 1 1 p 1 p 2 p x 2 x 1 p 2 α x 1 x 2 x 1 1 x 2 γ x 2 1 γ p 2 x 1 x 2 p 1 p 2 p x 2 x 1 x 2 p x 2 imple composition works in the typical cases [BAKER 1979, ENGELFRIET 1975] Tree Transducers in MT A. Maletti 36
108 Composition x σ σ p 1 p 2 x 1 x 2 x x 2 p 2 x 1 x 2 p 1 p α 1 1 p 1 p 2 p x 2 x 1 p 2 α x 1 x 2 x 1 1 x 2 γ x 2 1 γ p 2 x 1 x 2 p 1 p 2 p x 2 x 1 x 2 p x 2 imple composition works in the typical cases [BAKER 1979, ENGELFRIET 1975] Tree Transducers in MT A. Maletti 36
109 ummary Model \ Criterion EXPR YM PRE PRE 1 COMP Linear nondeleting TOP Linear nondeleting XTOP Linear nondeleting XMBOT Linear XMBOT General XMBOT reg.-preserving linear XMBOT invertale linear XMBOT Tree Transducers in MT A. Maletti 37
110 ummary Model \ Criterion EXPR YM PRE PRE 1 COMP Linear nondeleting TOP Linear nondeleting XTOP Linear nondeleting XMBOT Linear XMBOT General XMBOT reg.-preserving linear XMBOT invertale linear XMBOT Tree Transducers in MT A. Maletti 37
111 Implementation No implementation yet, Tree Transducers in MT A. Maletti 38
112 Implementation No implementation yet, ut stay tuned Tree Transducers in MT A. Maletti 38
113 ynchronous Tree-Adjoining Grammars -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N eria rya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ Tree Transducers in MT A. Maletti 39
114 yntax Definition (HIEBER, CHABE 1990) ynchronous tree-adjoining grammar (TAG) is G = (N, Σ,,, R) with a finite set R of sustitution rules adjunction rules Example (ustitution rule) X X Σ X 1... X k X i... X j Tree Transducers in MT A. Maletti 40
115 yntax Definition (HIEBER, CHABE 1990) ynchronous tree-adjoining grammar (TAG) is G = (N, Σ,,, R) with a finite set R of sustitution rules adjunction rules Example (Adjunction rule) X X Σ X X Tree Transducers in MT A. Maletti 40
116 Example Tree Transducers in MT A. Maletti 41
117 Example Used sustitution rule Tree Transducers in MT A. Maletti 41
118 Example 1 1 V 2 V 2 Used sustitution rule V V Tree Transducers in MT A. Maletti 41
119 Example 1 1 V 2 V 2 likes aime Used sustitution rule V likes V aime Tree Transducers in MT A. Maletti 41
120 Example V V likes N aime DT N les Used sustitution rule N DT N les Tree Transducers in MT A. Maletti 41
121 Example V V likes N aime DT N candies les onons Used sustitution rule N candies N onons Tree Transducers in MT A. Maletti 41
122 Example V V likes N aime DT N ADJ N les N ADJ candies onons Used adjunction rule N ADJ N N N ADJ Tree Transducers in MT A. Maletti 41
123 Example V V likes N aime DT N ADJ N les N ADJ red candies onons rouges Used sustitution rule ADJ red ADJ rouges Tree Transducers in MT A. Maletti 41
124 emantics Definition Computed transformation: τ G = {(t, u) T Σ T (, ) (t, u)} Tree Transducers in MT A. Maletti 42
125 Relation to tree transducers Illustration EMB HOM EMB HOM TG eval eval TAG Definition (HIEBER 2006) emedded tree transducer is a macro tree transducer: linear, nondeleting, deterministic, total 1-parameter: linear, nondeleting Tree Transducers in MT A. Maletti 43
126 Relation to tree transducers Illustration EMB HOM EMB HOM TG eval eval TAG Definition (HIEBER 2006) emedded tree transducer is a macro tree transducer: linear, nondeleting, deterministic, total 1-parameter: linear, nondeleting Tree Transducers in MT A. Maletti 43
127 Copying example Example T c T c a T c a a T c a a T c a a T c a Example T c T c a a a a Tree Transducers in MT A. Maletti 44
128 Copying example Example T c T c a T c a a T c a a T c a a T c a tring translation {(wcw R, wcw) w {a, } } Tree Transducers in MT A. Maletti 44
129 Basic properties Example (Copying translation) τ G = {(wcw R, wcw) w {a, } } Conseuences TAG are symmetric TAG do not preserve regularity (neither direction) Tree Transducers in MT A. Maletti 45
130 Basic properties Example (Copying translation) τ G = {(wcw R, wcw) w {a, } } Conseuences TAG are symmetric TAG do not preserve regularity (neither direction) Tree Transducers in MT A. Maletti 45
131 ummary Model \ Criterion EXPR YM PRE PRE 1 COMP Linear nondeleting TOP Linear nondeleting XTOP Linear nondeleting XMBOT Linear XMBOT General XMBOT reg.-preserving linear XMBOT invertale linear XMBOT TAG Tree Transducers in MT A. Maletti 46
132 Implementation XTAG [THE XTAG PROJECT 2008] Implements TAG, TAG Optimized for natural language applications Application of TAG Tree Transducers in MT A. Maletti 47
133 Implementation XTAG [THE XTAG PROJECT 2008] Implements TAG, TAG Optimized for natural language applications Application of TAG Tree Transducers in MT A. Maletti 47
134 References ARNOLD, DAUCHET: Bi-transductions de forêts. ICALP 1976 BERTEL, REUTENAUER: Recognizale formal power series on trees. Theor. Comput. ci. 18, 1982 ENGELFRIET: Top-down tree transducers with regular look-ahead. Math. ystems Theory 10, 1977 GALLEY, HOPKIN, KNIGHT, MARCU: What s in a translation rule? HLT-NAACL 2004 GRAEHL, KNIGHT: Training tree transducers. HLT-NAACL 2004 MAY, KNIGHT: TIBURON a weighted tree automata toolkit. CIAA 2006 ROUND: Mappings and grammars on trees. Math. ystems Theory 4, 1970 THATCHER Generalized 2 seuential machine maps. J. Comput. ystem ci. 4, 1970 Tree Transducers in MT A. Maletti 48
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