I understand that most acids are weak acids, i.e. they do not fully disassociate in solution. However, certain acids, such as $\ce{H2SO4}$, do. I have been unable to find out what the defining characteristic is that differentiates strong acids from weak ones.
For example, HCl is strong, yet both HF and HBr are weak (even though they're based on halogens as well). Shouldn't HF be even stronger?
What characteristic makes only a select few acids fully disassociate (and hence belong to the strong acid group)?