为语言创建 CFG

Question

I'm trying to create a cfg for this language L={(a^n)(b^m)(a^n) | m,n>0};

I tried putting S => aSba | e The words generated at the beginning works, but from a certain size on, the "b" starts to get in the way.

what's expected: aba, aabaa, aabbaa...

what's coming out: aSba, aaSbaa, aaaSbabaa...

Answer 1

Maybe that grammar:

S = E
E = a G a
G = E
G = b K
K = b K
K = ε

In the ABNF meta-syntax you can write it as:

S = "a" (S / 1*"b") "a"