# What is the maximum practical possible time complexity?

(see title)
practical means it must correspond to some useful algorithm
e.g print("helloworld"*graham(n)) is not something practical

i.e are there practical problems that can only be solved in tetration complexity or higher?

By "practical" you mean "less than exponential time"? Or just "it would be useful if we could solve this problem"? In the latter case there are many examples of exponential-time problems that would be useful to solve, e.g., traveling salesperson. (Look it up if you're unfamiliar with it.)

Cryptographic algorithms can be arbitrarily complicated. Leaving them aside, the biggest important problem I know about is matrix multiplication, θ(n³). (There is a really bizarrely complicated algorithm that's θ(n≈2.7), for which someone got a PhD.)

But I'm really not confident in all that. If string theory turns out to be true, physicists might have to multiply 12-dimensional matrices.

yes

yea i even know some cases where the complexity is (2^2^x)
But I'm asking are there ones over tetration

It's less of a problem than quantum simulation[using computers that don't normally work in very very very cold boxes]

The AI guys are already struggling with matrices thousands of times bigger than 12.

Oh. I don't know of any. (And they wouldn't be very practical!)

The most practical one I can think of is to cascade calculating the power set of a set n times.
But that won't be practical either:you dont calculate nested power sets that deep.

What algorithms are considered "useful"?

Ones that someone will pay you to implement! :~)

One of them is to scan a post and check if its pedantic!
/j