Simple finite state transducers

 

Transducers of various kinds form a core component of the lexical knowledge representation toolkit. The simplest kind of transducer, and the most widely used, is the finite state transducer (FST).

In this figure, we show a very simple (but nonetheless useful) FST that maps a sequence of atoms to the same sequence of atoms ($atom is a variable that ranges over atoms).

  

Figure 3: A very simple finite state transducer

We can implement this very simple transducer in DATR like this:

IDEM:
    <> ==
    <$atom> == $atom <>.

Under certain conditions, German word stems are subject to final consonant devoicing. The devoicing process itself simply maps voiced stops and fricatives to their voiceless counterparts and maps all other consonants to themselves. It is very easily and conveniently encoded as a finite state transducer:

Devoice:
    <b> == p
    <d> == t
    <g> == k
    <v> == f
    <z> == s
    <>  == IDEM.

Many German word stems also undergo a morphophonological process called umlaut under more or less complex conditions. The vowel change itself can be stated quite simply, however. As a first approximation, the following FST will do most of the relevant work:

Umlaut:
    <a>   == E
    <a:>  == E:
    <O>   == 9
    <o:>  == 2:
    <U>   == Y
    <u>   == Y
    <u:>  == y:
    <>    == IDEM.

[Note that we are using here the current standard SAMPA German characters for umlauted /O/ and /o:/. These differ differ from those shown in the earlier discussion of umlaut which was based on the CELEX SAMPA vowel inventory.]

Exercise 6014

Define an FST for English ablaut.

Exercise 6015

Define (i) an FST called VOWEL that maps sequences of SAMPA characters that begin with a vowel to T and all other such sequences to F, and (ii) one called ALVEOLAR that does the same for sequences that begin with an alveolar consonant.

Exercise 6016

Define an FST for the vowel lengthening that occurs in some German noun plurals (as in the final syllable of the plural form of Tutor, for example).

Exercise 6017

The FST given for German umlaut above does not say anything explicitly about what happens to diphthongs. Does it deal with them all correctly? If not, modify it so that it does.