Please answer question #4 in detail:

Problem 4: In this question, you are required to build a composite model for a traffic light system to be installed at a pedestrian crossing on a 2-way street, as shown in Fig. 1. The model for the entire system is to be built in the form of a Finite State Machine (FSM) by constructing parallel compositions of the three FSMs, provided in Fig. 2, for the individual lights in the system. Light 1 Light 3 Light 2 Figure 1: Three Lights to be installed. Light 1 is facing the other way. d1 d1 Stop Stop Walk Walk (a) FSM for Light (MI): 21 = {p, dl, d2} (b) FSM for Light2 (M2): 22 = {p, dl, d2} (c) FSM for Light3 (M3): 23 = {d1, d2} (p can be taken as the pedestrian button input, dl and d2 may be some external timer events, e.g., predefined delays) Figure 2: FSMs for Individual Lights (a) Which of the following compositions will you suggest for constructing the composite machine (give some explanation). Show your construction. (i) M1 || M2 || M3 (ii) M1 x M2 * M3 (iii) (M1 x M2) || M3 (iv) M1 (M2 || M3) (v) (M3 || M1)* M2 Problem 4: In this question, you are required to build a composite model for a traffic light system to be installed at a pedestrian crossing on a 2-way street, as shown in Fig. 1. The model for the entire system is to be built in the form of a Finite State Machine (FSM) by constructing parallel compositions of the three FSMs, provided in Fig. 2, for the individual lights in the system. Light 1 Light 3 Light 2 Figure 1: Three Lights to be installed. Light 1 is facing the other way. d1 d1 Stop Stop Walk Walk (a) FSM for Light (MI): 21 = {p, dl, d2} (b) FSM for Light2 (M2): 22 = {p, dl, d2} (c) FSM for Light3 (M3): 23 = {d1, d2} (p can be taken as the pedestrian button input, dl and d2 may be some external timer events, e.g., predefined delays) Figure 2: FSMs for Individual Lights (a) Which of the following compositions will you suggest for constructing the composite machine (give some explanation). Show your construction. (i) M1 || M2 || M3 (ii) M1 x M2 * M3 (iii) (M1 x M2) || M3 (iv) M1 (M2 || M3) (v) (M3 || M1)* M2