3. A "goods train" is defined to be a string of cars, which must begin with one or two engines. These are followed by one or more trucks, which are followed by one Guard Van. Example: E E T T T T G Non-goods trains: E G; E T T T; E E E T T T G

a. Write a DFA to recognize a goods train. Use E = engine, T = truck, G = guard van.

b. Write a regular expression that generates all legal goods trains.

c. Write a program that recognizes goods trains (says OK or not OK). (Input can be in any convenient form) . Run your program! Submit code (short please) and outputs. Use your DFA translate DFA to code.