Here we introduce a "polynomial-time reduction," which is one in which takes polynomial time (obviously). We also introduce the notion of NP-hardness and NP-completeness. We then show that if a problem is NP-complete, and is also in P, then P = NP.

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I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.