3. The Hamming distance between two bit strings z and y (notation: H(z,g) is the number of places at which they differ. For example H(011, 110)-2. (If lyl, then their Hamming distance is infinite e between z and A is the distance from z to the closest string in A: def VEA For any set A {0,1}* and k 0, define N027-10n), Ki(ooj) - the set of strings of Hamming distance at most k from A. For ex ample, N((000))-(00). N1((000)) = (000,001,010,100). and N2((00)) = {0.1)"-(111). Prove that if A (0,1)" is regular, then so is N,(A). (Hint If Ais accepted by a machine with states Q, build a machine for Na(A) witn states Q {0,1,2). The second component tells how many errors you have seen so far. Use sondeterminism to guess the string y A that the input string z is similar to and where the errors are.) 3. The Hamming distance between two bit strings z and y (notation: H(z,g) is the number of places at which they differ. For example H(011, 110)-2. (If lyl, then their Hamming distance is infinite e between z and A is the distance from z to the closest string in A: def VEA For any set A {0,1}* and k 0, define N027-10n), Ki(ooj) - the set of strings of Hamming distance at most k from A. For ex ample, N((000))-(00). N1((000)) = (000,001,010,100). and N2((00)) = {0.1)"-(111). Prove that if A (0,1)" is regular, then so is N,(A). (Hint If Ais accepted by a machine with states Q, build a machine for Na(A) witn states Q {0,1,2). The second component tells how many errors you have seen so far. Use sondeterminism to guess the string y A that the input string z is similar to and where the errors are.)