This is a KDF, a key derivation function that's built from HMAC.

So the derivation is 1, 4.

It was a kind of joke, because it's got a double derivation from the Greek.

Here I've shown another derivation starting with sentence.

What I've done here is what's called a derivation.

A derivation just means starting from some non terminal, follow the rules to derive a sequence of terminals.

And then I'm updating the derivation with the rule I used.

The way that's done, is using a mechanism called a key derivation function, KDF.

Instead of enumerating just the strings, we're going to enumerate strings along with their derivation.

If you don't remember or haven't seen this syntax before, this says I'm going to take the first and second values out of tokens and derivation and put them in the tuple (tokens, derivation).

Once we've enumerated all the derivations, we can check more than 1 derivation for that string.

The key derivation function would just work as follows. It would take as input the source key.

And this is a word that appears throughout early mathematics, such as this 10th century derivation of proofs.

This sort of maneuver with all these arrows is sometimes called a derivation because I was able to derive

For example, down here at the bottom, I have a derivation starting with number getting to the number 42.

I'll start the derivation and leave little gaps and ask you to pick one of those and plug it into the equation.

The derivation of those is beyond this class, but there are places we can look it up such as Barbara Ryden's book.

Now, to determine whether or not the grammar is ambiguous with regard to this string, I need to try and find another derivation.

If you skip, no one is ever going to know and I promise you derivation is not essential for using this formula over here.

First one is going to be P because I'm substituting S for P, and then I'm going to return the derivation, which is using just rule 0.

I left open the derivation, however, nine steps or where these nine bars that will turn into boxes very soon, and what you have to do is you have to pick from the 13 choices over here, the ones that fit best.

Now, you might not fully have gotten the derivation of this, and I recommend you to watch it again, but it's not that important for the progress in this class.

Finally, the derivation is surprisingly complicated, surprisingly involved but if you just do this few steps steps of computation it is possible to prove viral frankly some what complicated mathematical proof.

And later on when I do solve this problem, I'm going to refer to this derivation in the form of a list where I took rules 0, 2, and 5 to get ab.

Well, we collect data from satellites, from airplanes, from ground vehicles, from people.

It's from Decatur. From where?

Not from what, from whom.

Since I'm just going to start with start, the first value in the tuple is just going to be the string start or just the symbol start it's a 1 symbol string and an empty derivation since I haven't done anything yet.

I could come from here, from here, or from above.

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