Open course ware

[SQUEAKING] [RUSTLING] [CLICKING] MICHAEL SIPSER: All right, why don't we get started? It's 2:35, time to begin. So everyone, welcome back-- good to see you all. Well, at least a few of you-- glad that you're here. So let's see. Why don't I get a layout, as I usually do, where we have been, where we're going today. I'll talk a little tiny bit about the homework, because I've gotten a couple of questions on that. And then we'll jump in. So we have been talking about Turing machines, which is going to be our preferred model for the rest of the semester, since Turing machines are the model which we use to capture general purpose computing. And we looked at Turing machines in various variations on Turing machines-- multi-tapes, non-deterministic, and so on. It's a bit recapping the history of the subject, when people looked at a variety of different ways of formalizing the notion of algorithm. And they showed that all of those different...

[SQUEAKING] [RUSTLING] [CLICKING] MICHAEL SIPSER: OK, everyone. Let's get started. Welcome back to Theory of Computation lecture number six. So we have been looking at a number of different models of computation. And last lecture actually was an important one for us, because we shifted gears from our restricted models, finite automata, pushdown automata, and their associated generative models, regular expressions, and context-free grammars to Turing machines, which are going to be the model that we're going to-- which is the model that we're going to be sticking with for the rest of the semester, because that's going to be our model, as we're going to argue today, for a general purpose computer. So in a sense, everything we've been doing up till now or up until that point has been kind of a warm up. But it's been nevertheless has gotten a chance for us to introduce some important concepts that are used in practice and also will serve as good ex...