Some more specific thoughts:
- The discussion of finding a theory with the right balance between restrictiveness and expressiveness reminded me very much of Bayesian inference (find the hypothesis that has the best balance between simplicity and fit).
- My inner theoretical computer science geek was pretty happy about the discussion of problems and algorithms and tractability, and the like. When discussing determinism, though, I do think there's some wiggle room with respect to non-deterministic processes (i.e., those that guess when unsure). A number of acquisition models incorporate some aspect of probabilistically-informed guessing, with reasonable success.
- I thought the outline of phonological problems in particular (on p.9 of the first paper) neatly described a number of different interesting questions. I think the recognition problem is something like what psycholinguists would call parsing, while the phonotactic learning problem is what psycholinguists would generally call acquisition.
- I believe Heinz mentions that transducers aren't necessarily the mental representation of grammars, but a lot of the conclusions he mentions seems predicated on that being true in order for the conclusions to have psychological relevance. That is, if the mental representations of grammar aren't something like the transducers discussed here, how informative is it to know that a surface form can be computed in so many steps, etc.? Or maybe there's still a way to translate that kind of conclusion, even if transducers aren't similar to the grammar representation?
- The fact that two grammar formalisms (SPE and 2LP) are functionally the same is an interesting conclusion. What should then choose between them, besides personal preference? Ease of acquisition maybe?
- I really liked the discussion distinguishing simulations from demonstrations. I think that pretty much all of my recent models seem to fall more under the demonstration category.