Computer Science 5. Consider a language L over the binary alphabet. For any two binary strings x, y we say x, y are distinguishable by L if there exists a string w ∈ L such that exactly one of the strings xw, yw is in L. x, y are indistinguishable by L otherwise (denoted by idL. Prove that idL is an equivalence relation.

Consider the language L = {w010w | w ∈ Ld} Is this language recursively enumerable? Justify your answer

For any string w = w0w1w2 ...wn, the reverse of w, written wR, is the string in the reverse order, wnwn−1 ...w1w0. For any language L ⊆ Σ∗, we can define its reverse as LR = {wR | w ∈ L}. Show that if L is regular, then so is LR.

Let = {0, 1} and consider the following languages 1. LBOUNDED = {(M, x) : M is a TM, x € Σ*, M never moves its pointer more than |x| tape symbols away from the left endmarker |} 2. LDEC = {(M): M is a TM, L(M) is decidable} For each language, determine whether it is decidable or undecidable. If it is decidable, give a decision procedure which decides it. If it is undecidable, you must use Rice's theorem, if applicable, or a mapping reduction, otherwise. [Hint: Given some input string x, you may assume that the number of possible instantaneous configurations of a TM where the pointer never moves more than |x| tape symbols away from the left endmarker is at most |T||*|. (²[+¹). (¹).]

Question 5 Let I be the set of all even length binary strings. (So I is decidable.) Give an example of a language K ⊆ I with K undecidable. Here you need to define the set K and state your reasoning why the K you define is undecidable. Full explain this question very fast solution sent me step by step text typ work only