1. Run the Pushdown Automaton below on each of the given inputs. Give your answer as shown in part (a), as a sequence of machine states, as we did in class. A single machine state consists of x_y,q, s, where: x is the part of the input that has been read (consumed) already y is the remaining unread input qe Q is the current state of the finite state portion of the PDA ser is the stack contents, with the top of the stack on the left Note: E = {a,b,c} and r = {1, 2,$} a, 1 E, ES b, 1-1 c, 1-2 4 5 b, 1-1 b, 2-2 9 8 E, SE c, 2-8 a. Input: abc (The first two machine states have been done for you.) _abc, 4, _abc, 5, $ b. Input: abcbc C. Input: aabcbc d. Which of the inputs (a), (b), and (c) above does this PDA accept? e. Does this PDA accept the empty string, e? f. What language does this PDA accept? Give your answer using set notation