Introduction to Computational Linguistics

16. Finite State Morphology 59
Then it acts as a map from surface forms to deep forms. It will translate arm into
armR and arms into armS and armsR. The latter may be surprising, but the
machine has no idea about the lexicon of English. It assumes that s can be either
the sign of plural or the last letter of the root. Both cases arise. For example,
the word bus has as its last letter indeed s. Thus, in one direction the machine
synthesizes surface forms, and in the other direction it analyses them.
Now, let us make the machine more sophisticated. The regular plural is formed
by adding es, not just s, when the word ends in sh: bushes, splashes. If the
word ends in s then the plural is obtained by adding ses: busses, plusses. We
can account for this as follows. The machine will take the input and end in three
different states, according to whether the word ends in s, sh or something else.
(160)
〈0, a, 0, a〉, 〈0, b, 0, b〉, . . . , 〈0, z, 0, z〉,
〈0, a, 4, a〉, . . . , 〈0, r, 4, r〉, 〈0, t, 4, t〉,
. . . , 〈0, z, 4, z〉, 〈0, s, 2, s〉, 〈2, a, 4, a〉,
. . . , 〈2, g, 4, g〉, 〈2, h, 3, h〉, 〈2, i, 4, i〉,
. . . , 〈2, z, 4, z〉, 〈2, ε, 3, s〉, 〈3, ε, 4, e〉,
〈4, R, 1, ε〉, 〈4, S, 1, s〉.
This does not exhaust the actual spelling rules for English, but it should suffice.
Notice that the machine, when turned around, will analyze busses correctly as
busS, and also as bussesR. Once again, the mistake is due to the fact that
the machine does not know that busses is no basic word of English. Suppose
we want to implement that kind of knowledge into the machine. Then what we
would have to do is write a machine that can distinguish an English word from
a nonword. Such a machine probably requires very many states. It is probably
no exaggeration to say that several hundreds of states will be required. This is
certainly the case if we take into account that certain nouns form the plural differently:
we only mention formulae (from formula, indices (from index),
tableaux (from tableau), men, children, oxen, sheep, mice.
Here is another task. In Hungarian, case suffixes come in different forms. For
example, the dative is formed by adding nak or nek. The form depends on the
following factors. If the root contains a back vowel (a, o, u) then the suffix is nak;
otherwise it is nek. The comitative suffix is another special case: when added, it
becomes a sequence of consonant plus al or el (the choice of vowel depends in
the same way as that of nak versus nek). The consonant is v if the root ends in a
vowel; otherwise it is the same as the preceding one. (So: dob (‘drum’) dobnak