Let $\Sigma = {0, 1}$. Write CFG that generates the following language
{w | w contains at least two 1’s}
I'm not really sure how to write a CFG that generates a language, so this is my attempt…
S-> A1A1A
A->0A1|1A0|AA|$\epsilon$
I'm not sure about the start, maybe it should be
S->A1A
A->1A1|1A0|0A1|$\epsilon$
I really don't know what I'm doing, so any pointers for how I can solve this problem (and the next ones I need to solve) would be hugely helpful!
From what I can tell my answers make no sense since I don't really understand what I'm doing. Another example of what I have thought of as a possible solution is:
$S_0 \implies 0S_0 | 1S_1$
$S_1\implies0S_1|1S_2$
$S_2\implies0S_2|1S_2|\epsilon$
but I'm not sure if this works for more than two 1's or if it works at all for that matter.
Best Answer
Hint:
I hope this helps $\ddot\smile$