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 "Accept' or "Reject"$).($Input can be in any convenient form.$)$

Must use your DFA and translate DFA to code. You can decide how to represent the states and transitions in your program.

Programming language in Python.

Run your program! Submit code $($short please$)$ and outputs.