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Chiara Moraglia Branch of computational linguistics The study of mathematical structures and methods that pertain to linguistics. Combines aspects of computer science, mathematics and linguistics. Words: anchor Sentences : Cleaning fluid can be dangerous. Claire kicked the bucket. Machine translation that keeps in mind the problem of ambiguity. A sequence of reordering decisions and word translation decisions, each with a probability assigned based upon linguistic data. 2 main reordering models: 1) phrase-based models: re-align phrases (strings of words) 2) syntax-based models: can use tree transducers to permute trees (syntactic structure) with words as leaves http://people.csail.mit.edu/koehn/publications/tutorial2003.pdf Generalize the work on tree automata and tree transductions to non-deterministic models and explore the equivalence properties that were proven to hold in the deterministic case. A hierarchical collection of labeled nodes connected by edges, starting at a root node https://upload.wikimedia.org/wikipedia/commons/f/f7/Binary_tree.svg A tree transducer is a 5-tuple <F,H,Q, qin,R> where i) F is a functional signature of input symbols ii) H is a functional signature of output symbols iii) Q is a finite set of states iv) qin∈Q is the initial state v) R is a finite set of rules <q, φ> ζ where ζ is 1) <q’, ψ> 2) h(< q1, ψ1>,…,< qk, ψk>) Φ gives the conditions the current node must satisfy, Ψ says which node to go to from the current node (Courcelle & Engelfriet, 2012) A functional signature is a set of function symbols, each with an associated arity ρ(f) (the number of arguments the function takes on) E.g. f(x), ρ(f)=1 h(x,y,z), ρ(h)=3 (Courcelle & Engelfriet, 2012) i) F={f,a,b} where ρ(f)=2, ρ(a)=ρ(b)=0 ii) H= {a,b,ε} where ρ(a)=ρ(b)= 1, ρ(ε)=0 iii) Q={qin,q1,q2} iv) qin∈Q is the initial state v) R= 1) <qin, labf(x1)> <qin, down1> 2) <qin, labx(x1)^bri(x1)> x(< qi, up>) 3) <q1, True> < qin, down2 > 4) <q2, bri(x1)> < qi, up > 5) <q2, rt(x1)> ε 6) <qin, labx(x1)^rt(x1)> x(< q2, stay>) (Courcelle & Engelfriet, 2012) a or b(<a or b &1st child, >) q1 <f, > <True, > qin <1st child, > <a or b & root, stay> <2nd child, > a or b (<a or b & 2nd child, >) q2 ε <root, stay> input tree f a output tree a b b ε A tree transducer is deterministic if the state and the position in the tree uniquely determine what rule should be applied Otherwise, it is non-deterministic E.g. <qin, labf(x1)> <qin, down> <qin, labf(x1)> <q1, up> g(<f, >) qin <a, stay> a h(<f, >) Modified from (Fülöp, 1981) input possible outputs f g h g h f g h h g a a a a a The possible output trees would be assigned probabilities Then the words would be translated into the target language Courcelle, B., & Engelfriet, J. (2012). Graph Structure and Monadic Second-Order Logic. Cambridge: University Press. Fülöp. (1981). On attributed tree transducers. Acta Cybernetica, 5, p.261-279. Knight, K., & Koehn, P. What’s new in statistical machine translation [PDF document]. Retrieved from http://people.csail.mit.edu/koehn/publications/tutorial2003.pdf Tree (data structure). (n.d.). Retrieved from http://people.csail.mit.edu/koehn/publications/tutorial2003.pdf