Given an n variable boolean DNF formula and a number k, does this formula has satisfying input combination greater than k?. (0<=k<=2^n). Where input is infinite number of n tuples where repeating tuple is possible. For exampl. F(a,b) =ab + a'b. Input set is (11,00,11,01) and k=2. Answer is 3 here so decision says yes as 3>k. Can i define this problem in more formal way and prove that it is np/npc/ anything else. I am looking for suggestions specially for infinite number of tuples. I am aware of npc and reduction stuffs but need help to classify this problem properly.
Your problem can't be any easier than DNF-TAUTOLOGIES since that problem is produced by setting $k$ equal to $2^n$. Therefore your problem is NP-hard, just as DNF-TAUTOLOGIES is.