In chapter 3 of "Mathematical Linguistics" Kornai deals with phonology. It is very nice to see the mathematical theory of phonology laid out here, formalizing the autosegmental framework. I do have a few questions about this treatment, since it seems to rely heavily on the notion that there are phonemes and sound segments (consonants, vowels etc.) Autosegmental phonology is then formalized into a computational system using biautomata. It is emphasized that context-sensitive generating power is seemingly not needed for phonology, and that finite-state power is sufficient.
Kornai appears to state that we can solve the phonemicization problem for a language (meaning that the phonemic inventory is determined by the phonetic data). I thought Yuen-Ren Chao proved otherwise in 1934, and that this proof was formalized in Kracht 2003. For example, I fail to see how it is possible to prove that English affricates are actually single segments. Why aren't they sequences of two segments (a stop and a fricative)?
Another issue comes from speech perception research, where years of trying have failed to establish that people use consonants and vowels as perceptual units. Syllables appear to have much more traction in this regard. It is of course still desirable to transcribe syllables using segments, but this can be regarded as a convenient fiction, as was suggested already by Trager, I believe, in 1935. On the view just described, each syllable would then be formally treated as a sequence of distinctive features, with a certain ordering relation but without any timing slots.