Finite State Machines

A Finite State Machine:

• This is a machine that consists of a fixed set of states.
• Has a set of allowable inputs
• Has a set of possible outputs the are dependant upon the current state
• A FSM that has no outputs is a finite state automation

We can represent a FSM with finite state diagrams or state transistion tables.

A simple FSM would be a door. We can use:

To represent a state. you would put an arrow pointing to this if it was the starting state, or a smaller circle within it if it was the closed state(known as the accept state).

To represent a connector which shows the transistion between states.

You would write the transistion (input and output) on the connector.

So a basic door would have two states: Opened and Closed

and the inputs would be opening and closing              

So:

We can replace longer state names with: S1, S2, S3...  and then add a key to show what they are.

Also with some FSM we can add an output to each connector (this would go next to the input separated by a comma.

Decision Tables

This can be re written as pseudo

If X is greater than 6 AND Y is less than 7 OR Z is  equal to 3
Then  Output “Pass”
Else Output “Fail”