A time lower bound on linearizable READs

For a Sequentially Consistent implementation, there is no lower bound on either READ or WRITE. There exist implementations where the time required for either operation is 0. The only lower bound we’ve shown is that tREAD + tWRITE ≥ d, where d is the time required for a message to be transmitted between two neighboring processors. Nevertheless, in the previous lecture, we have a lower bound for the time taken for a linearizable implementation of READ. The technique we used to show that there was, indeed a lower bound on a READ was called a Shifting Technique. We created an execution, then shifted the order of some of the operations, and also used the existence of message delivery uncertainty to change the timing of message delivery. As a result, we obtained two distinct executions that processors could not tell apart, which produced a contradiction. We will use a similar Shifting Technique now, to prove a lower bound on WRITEs.