The "Grader" Problem for Context-Free Grammars is Undecidable.

The problem of determining whether two context-free grammars generate the same language is undecidable. This means that there is no algorithm for deciding whether a given context-free grammar generates a given language.
This means, in practice, that if you give a context-free grammar in a homework or test, it might be correct, and yet, it might be impossible to decide that it is correct. So, how can we grade it?
My answer is simple. If I give such a question on a homework or a test, I already have a fairly simple answer in mind. If the grader cannot see that your grammar is correct with a certain (small) finite time, then, right or wrong, your grammar is far more complex than necessary, and it will be marked wrong.
This same rule applies to all other problems where the "grader" problem is undecidable.