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PROFESSOR: We've mentioned the P equals NP question a number of times now as the most important question in theoretical computer science, and we've said that one way to formulate it is exactly to ask whether there's an efficient that is polynomial-time procedure to test whether or not a formula in propositional logic is satisfiable. Now, why is that such an important problem? We're not just logicians and we want to know whether or not some formula is satisfiable. How did it take on this enormous importance and apply to so many fields? And illustrating how you could use a satisfiability tester to factor efficiently is a good hint about why it is that all sorts of things reduce to SAT and why it, in fact, is such a centrally important problem. So let's suppose that we have a satisfiability tester and use it to find how to factor a number n. Now, the observation begins with how you use a SAT solver is that you can begin by writing or observing that it...