Reading 9 : Recurrences

In the last few readings we dealt with program correctness. We discussed correctness of nonrecursive as well as of recursive algorithms. In both cases, the proofs of correctness went by induction. As part of a proof of correctness, we show that the algorithm terminates. For example, we prove that a certain loop has to terminate after some number of iterations, or that the longest chain of recursive calls is finite. In practice, we usually want to know more than that an algorithm terminates. We want it to terminate in a reasonable amount of time. Thus, we want to prove termination in a stronger sense. We not only want to know that the algorithm terminates, but we also want to quantify how fast it terminates. This brings us to the question of program efficiency. In this reading, we use recurrences to argue efficiency of programs.