Let L be the set of non-empty even-length binary strings where the two middle symbols are different

Computer Science Nov 03, 2022

Let L be the set of non-empty even-length binary strings where the two middle symbols are different. To clarify: for a string W of length 2k, if we write W = w1 ... W2k, then the two middle symbols are wk and Wk+1. For example: 8, 00, 0110, 100011 are not in L, while 01, 0101, 100111 are in L. Your task: Using only the Myhill-Nerode Theorem, prove that L is not regular.