So starting with inference, yeah, this is basically just an example.

I don't know how you guys usually solve Sudokus.

I have to admit I'm rather stupid when it comes to Sudokus.

I basically just put all values that are there somewhere

in the corner and then rule them out, which is also

a kind of inference basically.

But yeah.

The point is if you just randomly now try out

all of the remaining things here,

this will not be exactly a smart thing to do.

And if you notice what usually normal people do

when they play Sudoku, you in some way already at this point

deduce that yeah, OK, there's only like technically there

are three values, but I need one of them here.

So probably it's only one of those two

and one of the other ones I need over here.

So actually this can only be one.

You do these kind of things in your head.

So let's basically try to model what we're doing there

in an abstract setting.

So as I said, the whole point of inference

in a constraint network is to come up with a way of constructing

a constraint network which is equivalent to our original

problem, i.e. they have the same solutions.

But in addition to it being equivalent,

we also want it to be more tight.

Those are the two notions.

So just that we get a feel for the whole thing.

So we can imagine we have a constraint problem like this.

We have three nodes.

We want them to be colored either red or blue.

And we have those two binary constraints

that tell us neither should v1 and v2 be the same,

and neither should v1 and v3 be the same color.

Now you can think about if we add this additional constraint

that we say also v2 and v3 shouldn't be the same.

Are these constraint networks equivalent?

Obviously they're not.

Why?

Well, whatever color I assign to v1,

I already know that v2 and v3 will

have to be the same color.

So basically this network has no solutions.

This one has two.

Which two?

Yeah?

Yeah, it's red, blue, red, or blue, red, blue.

Yeah, exactly.

And this one just doesn't work either way.

But as I just mentioned, basically we already