Which function suites more appropriately for the construction as long as? Is that expression used to, forgive the redundancy, express a necessary (not sufficient) condition? Or it is a material equivalence (bi-conditional)? Or it could mean any of the two concepts depending on the context it's used?
I think my last supposition is the correct. Based on these two examples:
As long as I've got my boots on, I might as well go out and get the firewood [taken from Merriam-Webster]
I will cooperate as long as I am notified on time. [taken from YourDictionary]
in the first case, the use of might suggests it's a necessary condition; while in the second case, the use of will cooperate suggest it is an if and only if.