And the idea is the following. Say we have a constraint satisfaction problem and the

only reason we're interested in this is because we're interested in the solutions. Right?

We're describing something that has some kind of a relation to the real world and we describe

that as a set of variables and domains and constraints. Now you can ask yourselves, can

we add constraints to that problem without changing the solutions? Okay? One thing you

immediately see if you add constraints, you're going, you might lose solutions but you're

never going to gain solutions. You might make a consistent problem inconsistent, losing

all the solutions or you might lose some of the solutions. Now the question, but that's

not something you want. You want to add constraints that help you go ahead, for instance in the

search. Remember if we have more constraints we might actually choose better variables.

Because the number of constraints on the variables tells us which one to pick. Okay? So it might

be that adding constraints lets our search algorithms perform better. And in this instance

here we can actually add a constraint without changing the set of solutions. If you think

about South Australia then you see that whatever you do here, these two determine that and

these two determine that. Okay? Or in other words, Western Australia and Queensland always

have to have the same colour. Okay? So what we're doing here is we're adding a constraint

and by and large this makes it easier for our search algorithms. Why? Well if we have

the additional constraint and we for some reason decide to make Western Australia blue,

we can immediately without choice actually also fill in Queensland. Eliminates an otherwise

triple choice into no choice at all. Okay? So adding constraints makes search easier.

Adding constraints that make it inconsistent make it very, very easy because you typically

notice directly or don't have to go very far down. But that's not what we want. We want

to actually conserve solvability and conserve all the solutions. Okay. And so the intuition

is that more constraints are better and we use the word a tighter description for that.

So what we want to do is we want to look at this, look at this constraint satisfaction

problem and we want to tighten up the description. Note, we're not searching. We're not even

talking about partial assignments. We're actually talking about transforming descriptions. Kind

of Shakespeare level. There's the real world and there's the description of the world by

Shakespeare and if you could kind of transform Shakespeare to do a better job in describing

the world, you could actually go from Hamlet plus plus and derive stuff from that. That's

the same thing we're doing here. We're not changing the world because we're not actually

changing the set of solutions. But we're tightening up the description which makes our life easier.

Okay.