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of hardness in English.

Peace base hard is the English expression.

There are people who insist that peace base is a difficult

expression, but that sounds kind of stupid.

So why not peace base hard?

I had already indicated a little bit how we do it.

You always need a mother of all peace base problems

which you then reduce to your target problem.

In the case of NP, it is the sat problem.

You could assume that everyone knows that the sat problem is NP-complete.

In fact, Rolf Bancker said that he sometimes in BFS also peace base hard from QBF.

Did he do that in the last time?

Two years ago?

No, probably not.

So, that means that today is our goal to do both.

I will keep myself a little bit.

Actually, I would like to say something about EL on Thursday.

So, quantified Boolean formulas.

This is an extension of the grammar of propositional logic.

So, here comes the whole grammar of propositional logic, as we know it,

and additionally this.

That's why it's called quantified Boolean formulas.

So, here I have an alquantum in it, which is a very harmless alquantum, namely an alquantum over Boolean values.

So, it has only two instances.

As usual, of course,

very hard here on my board.

So, if you look at it differently,

so, exist x, phi is of course a abbreviation for not for all x, not phi.

So, I have two quantums over Boolean values.

They are called what you expect.

So, that then says each...

Well, of course, now x is also a variable that can occur here.

We write the difference between non-quantified variables, we write the size as x, y and so on,

but they are otherwise exactly the same as the usual propositional atoms.