Introduction to Computational Linguistics

16. Finite State Morphology 58
Notice however that the transducer can be used to translate any language. In fact,
the image of a context free language under R T can be shown to be context free as
well.
Let us observe that the construction above can be generalized. Let A and B be
alphabets, and f a function assigning each letter of A a word over B. We extend f
to words over A as follows.
(157) f (⃗x · a) := ⃗x · f (a)
The translation function f can be effected by a finite state machine in the following
way. The initial state is i 0 . On input a the machine goes into state q a , outputs ε.
Then it returns to i 0 in one or several steps, outputting f (a). Then it is ready to take
the next input. However, there are more complex functions that can be calculated
with transducers.
16 Finite State Morphology
One of the most frequent applications of transducers is in morphology. Practically
all morphology is finite state. This means the following. There is a finite state
transducer that translates a gloss (= deep morphological analysis) into surface
morphology. For example, there is a simple machine that puts English nouns into
the plural. It has two states, 0, and 1; 0 is initial, 1 is final. The transitions are as
follows (we only use lower case letters for ease of exposition).
(158) 〈0, a, 0, a〉, 〈0, b, 0, b〉, . . . , 〈0, z, 0, z〉, 〈0, ε, 1, s〉.
The machine takes an input and repeats it, and finally attaches s. We shall later
see how we can deal with the full range of plural forms including exceptional
plurals. We can also write a machine that takes a deep representation, such as car
plus singular or car plus plural and outputs car in the first case and cars in the
second. For this machine, the input alphabet has two additional symbols, say, R
and S, and works as follows.
(159) 〈0, a, 0, a〉, 〈0, b, 0, b〉, . . . , 〈0, z, 0, z〉, 〈0, R, 1, ε〉, 〈0, S, 1, s〉.
This machine accepts one R or S at the end and transforms it into ε in the case
of R and into s otherwise. As explained above we can turn the machine around.