Is there any general technique for proving a problem NOT being NP-Complete?
I got this question on the exam that asked me to show whether some problem (see below) is NP-Complete. I could not think of any real solution, and just proved it was in P. Obviously this is not a real answer.
NP-Complete is defined as the set of problems which are in NP, and all the NP problems can be reduced to it. So any proof should contradict at least one of these two conditions. This specific problem, is indeed in P (and thus in NP). So I am stuck with proving that there is some problem in NP that can't be reduced to this problem. How on the earth can this be proven??
Here is the specific problem I was given on exam:
Let $DNF$ be the set of strings in disjunctive normal form. Let $DNFSAT$ be the language of strings from $DNF$ that are satisfiable by some assignment of variables. Show whether or not $DNFSAT$ is in NP-Complete.