I think you’re quibbling. Sharing state between independent tasks leads to nondeterminism. That’s the whole problem with shared state. Spooky action at a distance creates nondeterminism and even undefined behavior.
There are absolute claims to make, they just aren't the ones you're making. Determinism is an absolute claim of memoization. "Local rather than shared state" is simply not, no matter how many time you repeat it is.
Excluding shared state from memoization implies that you can't rely on the technique in parallel scenarios, which is just not true. I can think of more than a handful of DP problems where you can further optimize with parallelism if the function is modified to rely on shared state memoization. For example, the slew of problems that rely on the tabulation to simply fetch one value in the "previous row" and the value at the "previous column" of the current row. In practice, instead of iterating through rows and waiting to completely process them one at a time, you could simply start processing another row in parallel once you have just enough of the requisite "previous" data. This is absolutely valid DP. Some DP solutions even receive their tabulation. How does that not qualify as global?
If you thought "memoization is never shared", then in practice, not only your possibly very deterministic functions would end up solving the same problems over and over each time they're called, you would also deny yourself the opportunity of tremendous optimization techniques given by a guarantee of determinism.
> Many people confuse caching with DP. I’ve had that conversation too often.
This is the beginning of my thesis. Without this no other conversation is productive.
The problem with the DP space in specific and coding in general is that a substantial fraction of 'everyone' hears 'memoization' and immediately substitutes caching into their thought processes, "oh that's just caching, got it," and then believes they are productively contributing to the followup conversation when really all they are doing is confusing everyone else and themselves.
That's my beef, frustration, and frankly, institutional trauma. Equating them in your brain makes everything you say from them on practically useless.
You have a fair point about parallelism, but even here the sharing you illustrate is between parallel sub-problems, the 'sub' is IMO doing all of the work in that sentence. Versus me caching a header because you and I have the same account settings, only there's a bug because it's now showing you my unread message status due to incorrect sharing.
