NACLO 2025 - Problem LWhistle While You Work

Invitational round | 15 points | 20.51% | Problem statement | Official solution | Tags: Phonology

This is all in all a very, very tedious, eye straining, and honestly not much fun problem. It's quite obvious that the words are aligned by syllables: the initial consonant is dropped, while every subsequent onset consonant is aligned to a [h] or [q]. Let's write out the alignment:

né ko ti             ne no htá wee wa
 ó qò qóò             ó hò  qó hòò hóò

níi swi              ái kaa θo nía ni
 óò  hóò             óò qòò hó hóò hóò

né θwi hi
 ó  hò hóò

níe wi               o θáa skwaa né hkwe ya
 óò hóò              ò hóò   qóó hó   qò hóò

nía na nwi           ne mii náa ki
 óó hò hóò            ó hóó hóò qóò

ne ko twáa si ka     a si ká θoo na
 ó qó  qóó hò qóò    ò hó qó hòò hóò

nóo hi ka
 óó hò qóò

ne swáa si ka
 ò  hóó hò qóò

sáa ka
 óò qóò

                     ne sáe θí pe na
                      ò hóò hó qò hóò

níi htii θe          ne ne ma θó pe na
 óó qòò  hóò          ó hó hò hó qò hóò

ee hka tái naa hkwée ki
òò  qó qóò hòò   qóò qóò

The consonant rewrite rule is straightforward: if the consonant cluster contains {k, t, p} (i.e., voiceless stops), then it becomes [q]; otherwise it becomes [h]. Now we focus on the vowel rewrite.

Based on my careful character alignment above, it appears that the last vowel always becomes [óò]:

1. V → óò / __ #

All other single vowels turn into single mora, and double vowels turn into double mora. To understand how stress patterns are rewritten, we need to list out all contexts of each vowel (like we do in actual phonological analysis). Here I assume that the vowel rewrite can at most depend on the syllables before and after its syllable (in exams this needs to be by trial-and-error: first try the neighboring consonant; if it doesn't work then neighboring syllables).

Notice how stressed monophthongs only show up in the [ó] column. Complementary distribution is nice because it gives us a clear rule:

2. V́ → ó

Unfortunately, there still doesn't seem to be sufficient context for determining what unstressed single vowels turn into. We look ahead at one more syllable and only mark if it's the end of the word:

Notice how this additional word-end boundary marker only appears in certain categories, so there come our rules:

3. V → ò / __ σ # (penultimate unstressed monophthong syllable turns into ò)
4. V́V → óò / __ σ # (penultimate stressed diphthong syllable turns into óò)
5. VV → òò / __ σ # (penultimate unstressed diphthong syllable turns into òò)

Notice how in the [ò] column, the immediately following syllable always begins with {s, θ, h} (i.e., a voiceless fricative), and none of those in the [ó] column do. The same observation holds in the [òò] column—these are all unstressed diphthongs, and the unstressed diphthongs in [óó] are never followed by a voiceless fricative. This gives us a few more rules which fully determine monophthong rewrite and unstressed diphthong rewrite:

6. V → ò / __ {s, θ, h}
7. V → ó / otherwise
8. VV → òò / __ {s, θ, h}
9. VV → óó / otherwise

As for the stressed diphthongs, no obvious rule holds. This is kind of crazy but at this point we need to look ahead one more syllable and mark if it's the antepenultimate syllable (who even thought it's a good idea??).

Yes, I do expect to need to lookahead one syllable instead of one consonant; even two syllables sound reasonable, but 3 syllables is definitely too much. Anyway, once you do this, the rule is straightforward:

10. V́V → óó / __ σ σ # (stressed diphthongs in the antepenultimate syllable turn into óó)
11. V́V → óò / otherwise

To recap, I've reordered the rules and merged them:

1. V → óò / __ #
2. V́ → ó
3. V(V) → ò(ò) / __ σ #
4. V(V) → ò(ò) / __ {s, θ, h}
5. V(V) → ó(ó) / otherwise
6. V́V → óó / __ σ σ #
7. V́V → óò / otherwise
8. C → ∅ / # __ (i.e., initial consonant is dropped)
9. C…C → q / contains {k, t, p}
10. C…C → h / otherwise

Once we have these, the problem is straightforward: