# Find the Context Free Grammar

Let $\Sigma = \{a, b\}$. For each of the following languages, find a grammar that generates it.

(a) $L_1 = \{a^n b^m : n\geq 0, m>n\}$

(b) $L_1^3$

(C) $L_1^*$

I know the grammar for the language $L_1$, that is

$S \rightarrow aSb \mid bA$
$A \rightarrow bA \mid \epsilon$

• Please ask only one question per post! As for b,c: What have you tried? Where did you get stuck? We do not want to just hand you the solution; we want you to gain understanding. However, as it is we do not know what your underlying problem is, so we can not begin to help. See here for tips on asking questions about exercise problems. If you are uncertain how to improve your question, why not ask around in Computer Science Chat?
– Raphael
Aug 31, 2017 at 22:50

b) Introduce a new start symbol $S_1$ and a new production rule $S_1 \rightarrow SSS$
c) Introduce a new start symbol $S_2$ and a new production rule $S_2 \rightarrow S_2S \mid \epsilon$
• Can I write $L1^3$ as $L1^3$ = {$a^nb^m a^p b^q a^r b^s : n, p, r >=0, m>n, q>p, s>r$} ? how to write L1*? Aug 31, 2017 at 21:29
• Just Kleene closure of $L_1$ Sep 1, 2017 at 0:28