te for the class of Turing-decidable langug

2. Let A be a Turing-recognizable language consisting of descriptions of Turing machines, i.e., A = {(M1), (M2),...}, where every M; is a decider. Prove that some decidable language D is not decided by any decider M, whose description appears in A.

Let A be the language of binary strings of even length that are also palindromes. That is, A is a language over the alphabet S={0,1} and win A if and only if the length of w is even and w is equal to the reverse of w. Use the pumping lemma for regular languages to prove that A is not regular.

Consider the problem of the equivalence of the languages of two DFAs, formulate it as a language, and prove that language is Turing decidable by testing the two DFAs on all strings up to a certain size. Calculate a size will work for it.