Post correspondence problem

The Post Correspondence Problem (PCP) is a decision problem in formal language theory. It involves two lists of strings (or sequences of symbols). The question is whether there is a way to select strings from each list, in the same order, so that when these chosen strings are concatenated, they produce the identical overall string. PCP is significant because it is known to be undecidable—that is, there is no general method to always find such a sequence or determine that none exists for every possible case.