Problem 4 Let L be the language accepted by the pushdown automaton: M = (Q,E,r, 6, q, F) where: Q = {q, p}; E = {a, b, c, g};I = {A, D, E, L, P, R}; F = {q} and ổ is defined by the following...

pls solve this ques within 15-20 minutes with a complete explanation I'll give you multiple votes.

Extracted text: Problem 4 Let L be the language accepted by the pushdown automaton: M = (Q,E,r, 6, q, F) where: Q = {q, p}; E = {a, b, c, g};I = {A, D, E, L, P, R}; F = {q} and ổ is defined by the following transition set: (c) Write a complete formal definition of a context- free grammar that generates L. If such a grammar does not exist, prove it. [p, a, A, q, X] [q, 9, A, p, APPLE] [p, 9, D, p, X] p, c, E,p, X] [p, b, L, p, A] [p, 9, P,p, A] [p, b, R, q, X] [q, a, A, p, RED] (Recall that M is defined so as to accept by final state and empty stack. Furthermore, if an arbitrary stack string, say X1 ...X, € I* where n 2 2, is pushed on the stack by an individual transition, then the left- most symbol X1 is pushed first, while the rightmost symbol X, is pushed last.) (a) Write a regular expression that represents L. If such a regular expression does not exist, prove it. (b) Draw a state-transition graph of a finite-state automaton that accepts L. If such an automaton does not exist, prove it.