Assume two languages $L_1$ and $L_2$, both of which are non-context-free.
Let $L = L_1 \cap L_2$. Could $L$ be context-free?
Asked
Active
Viewed 1,676 times
2
-
1It's more interesting to ask whether the intersection of two context-free languages is context-free (though the answer is still negative). The union of two context-free languages is always context-free. So the only case remaining is the union of two non-context-free languages. What do you think, is it always non-context-free? – Yuval Filmus Oct 10 '13 at 02:42
1 Answers
6
The intersection could be empty.
David Richerby
- 81,689
- 26
- 141
- 235
-
+1 - it's funny how the trivial cases often help us more than one might expect, isn't it. – G. Bach Oct 09 '13 at 23:15