# Context free grammar to Chomsky's normal form

\begin{align*} S&\to AACD\\ A&\to aAb\\ C&\to aC\mid a\\ D&\to aDa\mid bdb\mid\varepsilon \end{align*}

I think that this grammar is infinite so it is not possible to convert it into cnf. Am I correct ?

## 1 Answer

Every context-free grammar can be converted to Chomsky normal form. Also, note that grammars are by definition finite: a grammar might describe infinitely many strings, but the grammar itself is finite.

• What will be it's cnf form ? – Adarsh Bahadur Dec 5 '18 at 20:08
• All the standard references explain how to convert a grammar to CNF. – David Richerby Dec 5 '18 at 20:12
• S is not terminating. That's what the confusion is. I'm unable to convert it. – Adarsh Bahadur Dec 5 '18 at 20:14