I'm studying for a finite automata & grammars test and I'm stuck with this question:
Construct a grammar that generates L:
L = {a^n b^m c^m+n|n>=0, m>=0}
I believe my productions should go along this lines:
S->aA | aB
B->bB | bC
C->cC | c Here's where I have doubts
How can my production for C remember the numbers of m and n? I'm guessing this must rather be a context-free grammar, if so, how should it be?
Seems like it should be like:
A->aAc | aBc | ac | epsilon
B->bBc | bc | epsilon
You need to force C'c to be counted during construction process. In order to show it's context-free, I would consider to use Pump Lemma.