Is following language context-free? Alphabet: {a,b,c,d} L = {w | w is not in {aabbc,abc,add}}
I think it is:
{aabbc},{abc},{add} are all regular.
Because of closure properties(Union) R = {w | w is in {aabbc,abc,add}} is also regular. Because of closure of complement (L is complement of R) L is also regular.
So L is regular, and since all regular languages are context-free : L is context-free.
You're right. In fact, every finite language is regular, and so is it's complement. They're context-free a fortiori.