1. Finite State Transducers for Morphological Parsing
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Finite State Transducers for Morphological Parsing
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2. Resumé FSAs are equivalent to regular languages
FSTs are equivalent to regular relations (over pairs of regular languages)
FSTs are like FSAs but with complex labels.
We can use FSTs to transduce between surface and lexical levels.
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3. Dotted Pair Notation 1) FSA recogniser for "fox" f o x
2) FST transducers for fox/fox; goose/geese
f:f
o:o
x:x
g:g
o:e
s:s
e:e
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4. Dotted Pair Notation (2)
By convention, x:y pairs lexical symbol x with surface symbol y
By convention, within the context of FSTs, we often encounter "default pairs" of the form x:x. These are often written as "x". g
o:e s e
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5. FSA for Number Inflection
How can we augment this to produce
an analysis?
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6. 3 Steps
Create a transducer Tnum for noun number inflection. This will add number and category information given word classes as input.
Create a transducer Tstems mapping words to word classes.
Hook the two together.
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7. Tnum example  ^ “lexical” +N +PL reg-noun-stem s # reg-noun-stem
“intermediate”
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8. 1. Tnum: Noun Number Inflection
multi-character symbols
morpheme boundary ^
word boundary #
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9. Tstems example # “intermediate” reg-noun-stem d:d o:o g:g f:f o:o x:x
“surface”
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10. Tstems example # “intermediate” m o:i u:ε s e s h e e p # “surface”
irreg-pl-noun-form
Tstems
m o:i u:ε s e s h e e p #
“surface”
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11. 2. Tstems Lexicon
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12. Hooking Together
There are two ways to hook the two transducers together
Cascading: hooking the output of one transducer with the input of the other and running them in series.
Composition: composing the two transducers together mathematically to create a third, equivalent transducer.
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13. Hooking Together: cascading
+PL
reg-noun-stem +N 
lexical
Tnum s
reg-noun-stem ^ #
intermediate
Tstems
dog fox  s #
surface
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14. Composition of Relations
Let R and S be binary relations.
The composition of R and S written R S is defined as:
(a,c)  R S if and only if (a,b)  R and (b,c)  S for all a,b,c
Transducers can also be composed
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15. Tnum o Tstem
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16. English Spelling Rules
consonant doubling: beg / begging
y replacement: try/tries
k insertion: panic/panicked
e deletion: make/making
e insertion: watch/watches
Each rule can be stated in more detail ...
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17. e Insertion Rule
Insert an e on the surface tape just when the lexical tape has morpheme ending in x,s,z,or ch and the next and final morpheme is -s
Stated formally   e [x|s|z|ch]^ __ s#
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18. e insertion over 3 levels
The rule corresponds to the mapping between
surface and intermediate levels
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19. e insertion as an FST
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20. Incorporating Spelling Rules
Spelling rules, each corresponding to an FST, can be run in parallel provided that they are "aligned".
The set of spelling rules is positioned between the surface level and the intermediate level.
Parallel execution of FSTs can be carried out:
by simulation: in this case FSTs must first be aligned.
by first constructing a a single FST corresponding to their intersection.
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21. Putting it all together
execution of FSTi
takes place in parallel
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22. Kaplan and Kay The Xerox View
FSTi are aligned
but separate
FSTi intersected
together
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23. Operations over FSTs
We can perform operations over FSTs which yield other FSTs.
Inversion
Union
Composition
The inversion of T, or T-1 simply computes the inverse mapping to T.
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24. Inversion T-1 T c a t ^ PL c a t ^ PL lexical lexical surface surface
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25. Inversion To invert a transducer Practical consequences:
we switch the order of the complex symbols, i.e. every i:o becomes o:i
or we leave the transducer alone, and slightly change the parsing algorithm.
Practical consequences:
Transducer is reversible
We can use the exactly the same transducer to perform either analysis or generation.
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26. Closure Properties of FSTs
Relations computed by FSTs are
closed under
inversion
union
composition
not closed (in general) under
intersection. However intersection is possible provided that we restrict the class of transducers.
complementation
subtraction
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