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: (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 of input one can easily check that these commands are the correct word acceptors.

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: (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.