Automata Theory Lesson II

In this lesson, we will be discussing the finite state machines, there examples and how they operate. At the end of this 
lesson, students should be able to understand the logic behind the finite state machines. Remember in our last discussion 
we introduced you to Automata Theory where we defined what an Automata Theory   is and the advantages of  studying Automata Theory .

So, what is a finite state machine?


A photo of passengers passing through the turnstile gate in a train station in South East Asia.
photo source: Google Images
A finite state machine also called a finite state automaton is a computational model that can be used to stimulate 
sequential logic and some other computer programs.
A finite state automaton or machine can be implemented where a system input can cause a certain change or changes in 
the state of a machine.

A very pefect example of a finite state machine is the turnstile gate system, this is a gate that opens or unlocks when a coin is inserted into it, after pushing the gate, the gate automatically locks up again returning back to its initial state. We can see that the state of the turnstile changes from "lock" to "unlock" immedietly a coin is inserted and the gate is pushed.

Schematic diagram of a finite state machine.
Another good example of a finite state machine is the automated teller machine (ATM machine) which gives access to 
transactions once an ATM card or any electronic debit/credit card is inserted, it also restricts transactions once the 
transaction is cancelled or ended. In this case we can see that there is a change of state from "restriction" to "access"
once a debited card is inserted into the machine.

Formal Definiton of a Finite State Machine.

An Automata Theory  can be represented by 5-tuple ($Q,\Sigma,\delta,q_0,F$) where
i) $Q$ isa finite set of states.

ii) $\Sigma$ is a finite set of alphabets or symbols of the automaton.

iii) $\delta$ is the transition function.

iv) $q_0$ is the initial state from where any input is processed $(q_0\in{Q})$
v) $F$ is a set of finate state of $Q(F\subset{Q})$.