I'll show it to you just for completeness' sake.

These gadgets come up a lot in NP completeness proofs.

The motion vector, just for completeness, will just be 0, 0, 0, 0.

In class, we keep brushing against Turing completeness, and it turns out that languages like

So, now we're in a good position to finally define this notion of NP completeness that I mentioned in the beginning of the unit.

One more property of the algorithms to consider is the property of completeness, meaning if there is a goal somewhere, will the algorithm find it?

This leads to a lack of completeness, which means there might be solutions to the navigation problem that this algorithm doesn't capture, but it does give us correctness.

I wanted to kind of express the notion of NP completeness and give you a chance to play with that a little bit, and in the homework, we're going to look at that in a little bit more depth.

Finally, just for completeness, let me write out the formula for the Gaussian distribution so the property of x and I'll sometimes write this instead of p of x, I'm going to write this as p of x semicolon Mu comma sigma squared.

Once you spend enough time designing algorithms to solve specific problems you start to realize that some problems don't seem to allow for efficient solutions. Unit Six covers the concept of NP Completeness. It doesn't actually give us a way to solve these problems any faster, but it does give us a pretty good indication when it might be okay to stop looking for an exact answer.