I'm exploring an algorithm that solves k-SAT. It uses a ton of preprocessing, so I'm thinking that this will be a circuit bounds.
Without knowing the runtime, I speculate on how quickly it will solve k-SAT instances. It will either solve all instances of k-SAT with probability $p$, or it won't be able to solve any instances. The runtime is based on $p$. Essentially, it runs in quasi-polynomial time.
So essentially, what we have is an algorithm that runs in time $2^{O((\log{n})^{c_1})}\cdot O(c_2 + q)$, and solves all instances with probability $\frac{2^q-1}{2^q}$, or it can't solve any instances. Here, $c_1$ and $c_2$ are constants.
It also requires space polynomial in $q$.
I'm trying to find what complexity class this is, and what is known about it.
SOME NOTES
Just to ensure I've described this correctly, I have an algorithm that either solves all instances, or it can't solve any. We can say it uses $2^{2^n}$ preprocessing. Then, it runs in time that is quasi-polynomial multiplied by a function of $q$.
THE QUESTION, AGAIN
What complexity class is this, and what is known about it?