How can I efficiently construct a CFG from a language I am new to CFG's and automata in general and I came across an exercise where I needed to construct a CFG for the language {a^m b^n | n &lt;= m + 3}.
So m can be infinitely bigger than n but n can only be up to 3 more bigger than m and they can be the same. I have no idea how to make a CFG for this.
What I came up with was:
S -&gt; AB | _ 
A -&gt; a | aa | aaa | C | _ 
C -&gt; aC | a | _
B -&gt; bB | b | _

But I think this is not even close...
Any help/tips/advice would be much appreciated!
The best way is to learn is to look at examples, and see how they work.
One of the simplest &quot;real&quot; context-free languages is $\{\; a^mb^n \mid n = m \;\}$
Its grammar is $S\to aSb\mid \varepsilon$.
Now add in steps, the extra 3, and the more than ...
$\{\; a^mb^n \mid n = m+3 \;\}$
$\{\; a^mb^n \mid n \le m+3 \;\}$