**Problem 1**:
Write a regular expression for the language L, over alphabet {0, 1, 2}, such that
every 0 that is not the last (rightmost) symbol is immediately followed by a 1, and every 1
that is not the last symbol is immediately followed by a 0.
By "immediately followed" we mean "with no intervening symbols. Thus, 010 is in L,
but 001 is not, because the first 0 is not *immediately* followed by 1.
021 is not in L for the same reason.

**Problem 2**: Describe an algorithm that converts an NFA A into a DFA whose
language is the *complement* of L(A). The complement should be taken with
respect to the alphabet of A. Give an informal argument for why your
construction works. You need not give a formal proof.

**Problem 3**:
Give a decision algorithm that tells whether a DFA A has the following property:
if string w is in L(A), then so is the string ww. For example, a DFA that accepts
the empty language has the property (vacuously). If L(A) is 0*, then it also has the
property. But if L(A) is all strings of 0's and 1's without two consecutive 1's,
then A does not have the property. In proof. note that w = 101 is in the language,
but ww = 101101 is not. You should give the algorithm and an intuitive argument why it works,
but again, no formal proof is needed.
A Hint is available and may be consulted at any time.