I'm stuck on these practice problems. If someone could help me solve them it would be great.
What is a contextfree grammar for the langauge $L = \{a^i b^j c^j d^i \mid i,j \ge 0\}$
The following claim is false. Explain why it is false and make a modification to the claim so that it becomes true.
Claim: Let $N = (Q, \Sigma, \delta, q_0, F)$ be an NFA with a unique final state, $F = \{q_f\}$. Suppose we add the production $\delta(q_f, \lambda) = q_0$ to $\delta$. Then the resulting NFA accepts the language $L(N)^*$
Give a regular expression for the language $L = \{w \in \Sigma^* \mid 1 \le |w| \le 3\}$. Here $\Sigma = \{a,b\}$.