The Hamming distance between two bit strings z and y (notation: H(x, y)) is the number of places at which they differ. For example, H(011,110)-2. (Ifl ^ 1yl, then their Hamming distance is infinite.) If x is a string and A is a set of strings, the Hamming distance between r and A is the distance from x to the closest string in A: H(x, A) del min H(a,y). VEA For any set A C 10,1}* and k 2 0, define def the set of strings of Hamming distance at most k from A. For ex- ample, No(00[000), Ni(000) 000, 001,010, 100), and N2 (000,13 Prove that if A C 0,1]* is regular, then so is N2(A). (Hint: If A is accepted by a machine with states Q, build a machine for N2(A) with states Q x [0,1,2). The second component tells how many errors you have seen so far. Use nondeterminism to guess the string y A that the input string z is similar to and where the errors are.)