Let's say that my CPU can be made arbitrarily faster (or I can become arbitrarily patient waiting for the CPU to complete its task), and let's say that my memory (e.g. RAM) can be made arbitrarily larger. I.e. none have any limits/caps.
My question is, what is the tightest law, or theorem, that maps change in space/ram into change in time/cpu?
E.g. I'm looking for something like: regardless of the hardware used, for a given algorithm $a$, if we (say) double the RAM, the CPU time will shrink in half.
Of course the above is just an example, and not meant to be exactly like it. I am simply looking for the latest theories in this area that give the tightest bounds on mapping space-memory relationship.