Boolean satisfiability problem

Here's the simple version.

There's a famous computer science problem called SAT or Boolean Satisfiability.

So imagine you have a bunch of switches that can be turned on or off along with a set of rules.

Your goal is to find the combination of switches that satisfies all these rules.

There's an optimal strategy.

So first, so what is worst case analysis? So I was describing the SAT problem earlier and the algorithmic problem you want to solve is given any formula you want to decide, is it satisfiable or not? Yeah.

Now, what's crucial there is that when I'm asking you to solve that algorithmic problem, I'm not telling you anything more about the structure of the formula.

I'm not telling you, you know, these are the size of the clauses.

And we use that to great effect for our cryptography systems.

But it does seem like in practice, a lot of problems are much easier than we give them credit for.

So for things like SAT, one of the places where they come up is in compilers and register allocation.

And SAT solvers are amazingly effective at solving those kinds of SAT problems.

That's the first.

The next one, SAT, this is for satisfiability.

And this is the special case of CSP when all the domains are just Boolean.

Every variable has just two possible values, while the CSP allows D-ary things.

And each of these is sort of equal power.

I can take any CSP, and I can encode it.

I can convert it to a SAT problem in several ways.

I can convert it to an XCC problem in several ways.