Finite State Transducers The machine model we will study for morphological parsing is called the finite state transducer (FST) An FST has two tapes –input tape (with an input alphabet) –output tape (with an output alphabet)

Formal definition of FST (from text) M = (Q,  q0, F,  ), where –Q is a finite set of states –  is a finite alphabet of complex symbols (i.e. pairs of input-output symbols).  = { i:o | i is an input tape symbol and o is an output tape symbol} –q0  Q is the initial state –F  Q is a set of final (accepting) states –  Q 

Example We want to be able to parse words (recover structure for them) including such words as goose (which is ambiguous): –goose  [goose +N +SG] or [goose +V] –geese  [goose +N +PL] –gooses  [goose +V +3SG]

Components of a morphological parser lexicon: morphemes (stems and affixes) together with category information morphotactics: rules of morpheme order orthographic (spelling) rules: rules of changes in spelling when morphemes combine

Lexicon for FST The lexicon can be modelled using two levels: –Surface form (e.g. geese) –Underlying form (e.g. [goose +N +PL]) This will allow lexicon to handle irregular forms Example lexicon on next slide

Example lexicon f:f o:o x:x[fox +N +SG] c:c a:a t:t[cat +N +SG] g:g o:o o:o s:s e:e[goose +N +SG] or [goose +V] g:g o:e o:e s:s e:e[goose +N +PL] g:g o:o o:o s:s e:e  :d [goose +V +3SG] s:s h:h e:e e:e p:p[sheep +N +SG] or [sheep +N +PL] m:m o:o u:u s:s e:e[mouse +N +SG] m:m o:i u:  s:c e:e [mouse +N +PL]

Generation example: foxes foxes fox+N+PL fox^s#

FST for [fox +N +PL]  fox^s# q0q1q2q5q6q7 f:fo:ox:x +N:  +PL:^s#

FST for E-insertion rule q0q1q2q3q4 q5 ^:  # other z,x,s z,x # other # other # ^:  s  :e s “other” means any symbol except “s”, “x”, “z”, “^”, “  ”, “#”

Generation example: foxes fox^s# fox+N+PL foxes