Finite Automata with Output (Set 5)
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 {0, 1} as input and produce βAβ as output if the input contains β1β as the substring or the input string starts with β1β or ends with β1β.
That is here we have,
Ξ = {0, 1} and
Ξ = {A, B}
where Ξ and Ξ are the input and output alphabet respectively.
The required Moore machine is constructed below:-
Explanation:
In the above diagram, the initial state βXβ on getting β0β as the input it remains in the state of itself and prints βBβ as the output and on getting β1β as the input it transits to a state βYβ and prints βAβ as the output. The state βYβ on getting β1β as the input it remains in the state of itself and prints βAβ as the output and on getting β0β as the input it comes back to the state βXβ and prints βBβ as the output.
Thus finally above Moore machine can easily give βAβ as the output on getting β1β as input substring.
The required Mealy machine is constructed below:-
Explanation:
In the above diagram, the initial state βXβ on getting β0β as the input it remains in the state of itself and prints βBβ as the output and on getting β1β as the input it transits to a state βYβ and prints βAβ as the output. The state βYβ on getting β1β as the input it remains in the state of itself and prints βAβ as the output and on getting β0β as the input it comes back to the state βXβ and prints βBβ as the output.
Thus finally above Mealy machine can easily give βAβ as the output on getting β1β as input substring.
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