# TOC | 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’.

## Recommended Posts:

- TOC | Finite Automata with Output (Set 6)
- TOC | Finite Automata with Output (Set 11)
- TOC | Finite Automata with Output (Set 5)
- Compound Finite Automata (FA)
- TOC | Designing Deterministic Finite Automata (Set 10)
- TOC | Designing Deterministic Finite Automata (Set 8)
- TOC | Designing Deterministic Finite Automata (Set 7)
- TOC | Designing Deterministic Finite Automata (Set 6)
- TOC | Designing Deterministic Finite Automata (Set 11)
- TOC | Designing Non-Deterministic Finite Automata (Set 5)
- TOC | Designing Non-Deterministic Finite Automata (Set 4)
- TOC | Designing Non-Deterministic Finite Automata (Set 1)
- Practice problems on finite automata
- Practice problems on finite automata | Set 2
- TOC | Designing Deterministic Finite Automata (Set 2)

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