Construct a grammar for $\{a^n(bc)^m : m,n \ge 1, m < n/2\}$ I'm new to writing languages in context-free or regular grammar, so I'm struggling how to do this one. It is a bit more complicated that simpler ones I've practiced doing. The problem is to construct a grammar for the following language:
$$\{a^n (bc)^m \in \{a, b, c\}^* \mid m, n \ge 1 \land m &lt; n/2\}$$
An explanation of how to start and go through the language would be really helpful.
Let $n = n'+1$, $m = m'+1$. Then $m &lt; n/2$ translates to $n'+ 1 &gt; 2(m+1)$, i.e. $n' \geq 2m'+2$. Therefore we can write the language as
$$
\{ a^{1+2m'+2+k}(bc)^{1+m'} : m',k \geq 0 \} =
\{ a^3 a^k (a^2)^{m'} (bc)^{m'} bc : m',k \geq 0 \}.
$$
You take it from here.