For each of these problems, describe an algorithm which solves it. (Or, if you think there is no such algorithm, you can prove it.) Dont worry about efficiency of the algorithms.

1) Given a DFA M and a string w, does M accept w?

2) Given a DFA M, is the language M accepts, L(M), infinite?

3) Given a DFA M, is L(M) = ?

4) Given DFAs M1 and M2, is L(M1) = L(M2)?

5) Given DFAs M1 and M2, is L(M1) L(M2) = ?

6) Given DFAs M1 and M2, is L(M1) L(M2)?