I don’t think it was formally proven that OL is strictly more powerful than PL but we were given examples that convinced us.

But you are certainly right: You have to draw the line somewhere, and I can’t say that most students can use Ogden’s Lemma after that course.

I would say that Ogden’s lemma is not typically taught in an undergraduate course in formal language theory. Considering that its proof is obtained just by a careful observation of a proof of the pumping lemma for CFL, I imagine that Ogden’s lemma can be one of the possible advanced topics covered in such a course. But clearly we have to draw a line somewhere.

To fully motivate Ogden’s lemma, we would like to argue that it is strictly stronger than the pumping lemma. However, showing that the non-context-freeness of some language cannot be proved by the pumping lemma seems to be beyond the scope of an undergraduate course. This might be one of the reasons why Ogden’s lemma is not taught in many undergraduate courses.

$\{xx’: x, x’$ are of equal length, and disagree in at most 2 positions$\}$.

Also, consider the kind of algorithmic problem that Cem Say’s example suggests. We’re given an expression in some grammar augmented with variable exponents (i, j, k, etc.), along with some relations between these–perhaps just inequalities, perhaps also arithmetic relations. Question: is the resulting language regular? Context-free?

Obviously with a rich-enough grammar or set of exponent-relation constraints this is going to be undecidable. But what is the simplest specification vocabulary for which this problem is undecidable?

For what it is worth, I have taught this material at a few universities in Europe and I have never taught Ogden’s Lemma. In fact, the Pumping Lemma for CFL is already hard enough for most undergraduate students.

You write: “the fact that there is a “stronger version” of pumping lemma for CFL should be handed to all students.” I guess that this is correct for theory-oriented graduate students, but I believe that in an undergraduate course our main goal should be to give students a flavour of the material and entice them towards further study of the material in the future. Less is actually more. (For instance, we do not teach students many different versions of the Pumping Lemma for regular languages.)

I wonder; is Ogden’s Lemma not typically taught in undergrad theory lectures? I know it was presented to us. I always have to look its exact formulation up, but the fact that there is a “stronger version” of pumping lemma for CFL should be handed to all students.