<blockquote>
  <p>Can we have more than one Deterministic Finite Automata (DFA) diagrams for a set of strings?</p>
</blockquote>

<p>Of course!</p>

<p><a href="//en.wikipedia.org/wiki/DFA_minimization" rel="nofollow noreferrer">There's also an algorithm to minimize a deterministic finite automata into a <em>minimal deterministic finite automata</em></a>. The existence of such algorithm is a proof that for most, if not all, sets of strings, many DFAs can be defined.</p>

CC BY-SA 4.0
2019-09-25T16:55:50.727Z
After reading I must agree. Thanks for answering my somewhat obvious question @john
Aaron Miller
CC BY-SA 4.0
2019-09-25T16:31:21.160Z
2019-09-25T16:31:21.160Z
53693
<p>Much like many math equations can be simplified. I am wondering if Deterministic Finite Automata diagrams can equal each other while some may be more simplified than others. I am following the <a href="https://www.youtube.com/watch?v=_2cKtLkdwnc" rel="nofollow noreferrer">youtube video</a> and I am wondering if the graph that I drew with pencil and paper would also be correct. Given the Prompt:</p>

<p><code>Construct a DFA that accepts any strings over {a,b} that does not contain the string aabb in it</code>.</p>

<p><a href="https://i.sstatic.net/ZPLA7.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ZPLA7.png" alt="enter image description here"></a></p>

<p><a href="https://i.sstatic.net/46m69.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/46m69.jpg" alt="img1"></a></p>

<automata-theory><fsm>
Can we have more than one Deterministic Finite Automata diagrams for a set of strings?
Aaron Miller
# Can we have more than one Deterministic Finite Automata diagrams for a set of strings?

(Asked by: username_0 on 2019-09-25)

Much like many math equations can be simplified. I am wondering if Deterministic Finite Automata diagrams can equal each other while some may be more simplified than others. I am following the [youtube video](https://www.youtube.com/watch?v=_2cKtLkdwnc) and I am wondering if the graph that I drew with pencil and paper would also be correct. Given the Prompt:

`Construct a DFA that accepts any strings over {a,b} that does not contain the string aabb in it`.

[![enter image description here](https://i.sstatic.net/ZPLA7.png)](https://i.sstatic.net/ZPLA7.png)

[![img1](https://i.sstatic.net/46m69.jpg)](https://i.sstatic.net/46m69.jpg)

**Tags:** automata-theory, fsm

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## 1 answers

### Answer by username_1 on 2019-09-25. Score: 2 | Accepted answer

> Can we have more than one Deterministic Finite Automata (DFA) diagrams for a set of strings?

Of course!

[There's also an algorithm to minimize a deterministic finite automata into a *minimal deterministic finite automata*](//en.wikipedia.org/wiki/DFA_minimization). The existence of such algorithm is a proof that for most, if not all, sets of strings, many DFAs can be defined.

> **Comments:**
> **username_0**: After reading I must agree. Thanks for answering my somewhat obvious question @john  

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