As Derek Holt suggested in a comment, it seems Thurston was indeed thinking of word acceptors that returned normal forms for elements of automatic groups. From a 1989 research report of his titled [Groups, tilings and finite state automata:][1] (pg. 41)

> A good example is the Unix utility `egrep`. The word acceptor for Z, for instance, could
be specified by the regular expression
`a*|A*`
where the symbol `*` denotes zero or more repetitions of the preceding object,
 and the
symbol `|` means ‘or’. The command `egrep '^a*|A*$'` 
prints out all lines of its inputs which are accepted by WA $\dots$

He goes on in page 42:

> For instance, a word acceptor which accepts only words in reduced form for
the free group $\langle ab|\rangle$ is illustrated in 11.3. The corresponding `egrep` command is
`egrep '^(b+|B+)?((a+|A+)(b+|B+))*(a+|A+)?$'` $\dots$


With a text file as input one can easily check that these commands are the correct word acceptors.

  [1]: http://timo.jolivet.free.fr/docs/ThurstonLectNotes.pdf