Question 1.11: Prove that every NFA can be converted to an equivalent one t...

Let  N = (Q,\Sigma ,\delta ,q_{0}, F ) be any NFA. Construct an NFA N^{\prime } with a single accept state that recognizes the same language as N. Informally, N^{\prime } is exactly like N except it has ε-transitions from the states corresponding to the accept states of N, to a new accept state, q_{accept}. State q_{accept} has no emerging transitions. More formally, N^{\prime } = (Q\cup \left\{q_{accept} \right\}, \Sigma ,\delta ^{\prime }, q_{0},\left\{q_{accept} \right\} ), where for each q ∈ Q and a ∈ \Sigma _{\epsilon }

and \delta ^{\prime } (q_{accept} ,a)= \phi for each  a\in \Sigma _{\epsilon }