Peter Linz Edition 4 Exercise 7.2 Question 11,12,13 (Page No. 195)

Question

11. Show that the npda in Example 7.8 accepts L (aa*b).
12. Find the grammar that generates Example 7.8 and prove that this grammar generates the language L (aa*b).
13. show that the variable ($q_0zq_1$) is useless. (see page no. 191-193)

Example 7.8 : Consider the npda with transitions

                        $\delta(q_0,a,z)=${$(q_0,Az)$},

                        $\delta(q_0,a,A)=${$(q_0,A)$},

                        $\delta(q_0,b,A)=${$(q_1,\lambda)$},

                        $\delta(q_1,\lambda,z)=${$(q_2,\lambda)$}.