Finite Automata with Output (Set 3)

Prerequisite: Mealy and Moore Machines, Difference between Mealy machine and Moore machine
In this article, we will see some designing of Finite Automata with Output i.e, Moore and Mealy machines.

Problem: Construction of the machines that take set of all string over {a, b} as input and count number of substring ‘a’.
That is here we have,
Ε = {a, b} and
Δ = {0, 1}
where Ε and Δ are the input and output alphabet respectively.
The required Moore machine is constructed below:-

Explanation:
In the above diagram, the initial state ‘X’ on getting ‘b’ as the input it remains in the state of itself and print ‘0’ as the output and on getting ‘a’ as the input it transits to a state ‘Y’ and prints ‘1’ as the output. The state ‘Y’ on getting ‘a’ as the input it remains in the state of itself and prints ‘1’ as the output and on getting ‘b’ as the input it comes back to the state ‘X’ and prints ‘0’ as the output.
Thus finally above Moore machine can easily count substring ‘a’ i.e, on getting ‘a’ as the substring it gives ‘1’ as the output thus on counting number of ‘1’ we can count the number of substrings ‘a’.

The required Mealy machine is constructed below:-

Explanation:
In the above diagram, the initial state ‘X’ on getting ‘b’ as the input it remains in the state of itself and print ‘0’ as the output and on getting ‘a’ as the input it transits to a state ‘Y’ and prints ‘1’ as the output. The state ‘Y’ on getting ‘a’ as the input it remains in the state of itself and prints ‘1’ as the output and on getting ‘b’ as the input it comes back to the state ‘X’ and prints ‘0’ as the output.
Thus finally above Moore machine can easily count substring ‘a’ i.e, on getting ‘a’ as the substring it gives ‘1’ as the output thus on counting number of ‘1’ we can count the number of substrings ‘a’.