When teaching educators:
With students, we deliberately let them find out as they do the activity that arrows and labels are important, because in the process they will invent for themselves the notation of a finite state automata!
Without the As and Bs it would have been confusing as to which line represented which train.
Without arrows it would have been easy to forget which train went to the station and which was leaving it.
Don't be too hard on yourself, we didn't say at the beginning that you couldn't get back to your starting point on the same train you took away from it.
You can see how having arrows on each line and labelling them with As or Bs makes it easier to describe the final successful route from the Airport Station to the Harbour Station.
These lines with arrows represent what are called 'transitions'.
This map represents a common idea used by computer scientists for processing complicated input for a computer, and is not really for mapping train stations (in case you hadn't realised!).
We are now going to explore this notation and how it relates to computer science.
You can see in the image that each station has a circle around it.
The circle indicates that this is a 'state'.
The starting state (Airport Station) is shown with an arrow pointing at it labelled 'Start'.
The final destination (Harbour Station) is indicated with a double circle around it.
This is called the 'final', or 'accepting' state.
It is the state that says “Yes, your sequence (string) is in this machine's language, it works.”
In other words, in our example any string of As and Bs that gets us from the Airport Station to the Harbour Station is accepted as valid, i.e. will get us to the 'accepting' state.
It's important to note that with a finite state automata, we're not worried about the shortest way to get to the accepting state, but just whether or not you end up there for a given string.
Now that you have this map, I am going to give you a string of As and Bs.
Each A or B is a transition, (railway line), between the states (stations).
The starting state is Airport Station like before, and we'll be transitioning to other states.
I'll give you the string, you tell me which state we end up at, that is, which train station.
To make it quicker, you only need to type its number or the first three letters of the station.