The Post correspondence problem is an undecidable decision problem that was introduced by Emil Post. Because it is simpler than the Halting problem and the Entscheidungsproblem it is often used in proofs of undecidability.
Informally the problem can be described as follows. Given a dictionary that contains pairs of phrases, i.e., a list of words, that mean the same, decide if there is a sentence that means the same in both languages.