Designing CFG that accepts $a^n b^m c^p$ where $n=m+p+2$

Asked May 22 '21 at 23:21

Active May 22 '21 at 23:29

Viewed 46 times

I have generated the CFG of $a^n b^m c^p$ where $m = n+p+2$:

$S \rightarrow ASC \mid \varepsilon$

$A \rightarrow aAb \mid \varepsilon$

$C \rightarrow bCc \mid \varepsilon$

I have been trying $a^n b^m c^p$ where $n=m+p+2$ but cannot figure out how to represent $n=m+p+2$. Any hint would really be appreciated.

edited May 22 '21 at 23:29

Nathaniel

asked May 22 '21 at 23:21

Hasnat

3

Does this answer your question? How to prove that a language is context-free? You should look at examples. – Nathaniel May 22 '21 at 23:27
I tried it myself and this was my solution Is this correct? S->abSA | a , C -> Ac | NULL – Hasnat May 22 '21 at 23:39
No, because 1) $A$ is not rewritten 2) it can create $abaA$. – Nathaniel May 22 '21 at 23:51
Thanks a lot. I think I found the answer. Here it is: $S->$C$S | aa , $C->$A$C | NULL , $A->$B$A | a , B->a B b | NULL. Please, do tell me if its correct. Thanks a lot – Hasnat May 23 '21 at 00:16
3

The grammar in your question recognises $a^nb^mc^p$ where $m = n + p$, not $m = n + p + 2$. Although it's easy to fix. – rici May 23 '21 at 04:43

0 Answers0