<p>Thanks to the hint given by @Micheal Wehar, I looked into Cartesian Product constructions and Intersections and I came across this answer:</p>

<p><a href="https://stackoverflow.com/questions/7780521/how-to-use-the-intersection-construction-to-form-a-dfa">https://stackoverflow.com/questions/7780521/how-to-use-the-intersection-construction-to-form-a-dfa</a></p>

<p>which seems to answer the question appropriately. </p>

CC BY-SA 3.0
2018-01-15T04:59:34.113Z
In the future, please try [CS Stackexchange](https://cs.stackexchange.com/) for these non-research-level questions.
Caleb Stanford
CC BY-SA 3.0
2018-01-14T18:33:14.757Z
2018-01-14T18:33:14.757Z
Quinty
<p>I am trying to design a DFA s.t. The set of strings in x ∈ {0, 1}∗
such that the number of zeros is a multiple of 3 and the number of one's is even.</p>

<p>My idea was to create two Machines M1 = (Q1, Σ, δ1, q1, F1), M2 = (Q2, Σ, δ2, q2, F2). </p>

<p>The first M checks if the number of 1's is even, and the second checks if the number of zeros is a multiple of 3. </p>

<p>If M1 accepts and M2 accepts, that is M1 intersection M2, then M accepts the input A. Is this a valid representation of a possible DFA, or am I supposed to make a singular Machine M s.t. the DFA accepts the input A? </p>

CC BY-SA 3.0
2018-01-14T18:22:29.833Z
You should try using the Cartesian product construction.  It will allow you to build a new automaton based on M1 and M2's state diagrams.  :)
Michael Wehar
CC BY-SA 3.0
2018-01-15T04:59:38.790Z
In the future, please try [CS Stackexchange](https://cs.stackexchange.com/) for these non-research-level questions.
Caleb Stanford
<automata-theory><dfa>
When designing a DFA, am I allowed to design two separate Machines and perform an Intersection on them?
Quinty
# When designing a DFA, am I allowed to design two separate Machines and perform an Intersection on them?

(Asked by: username_0 on 2018-01-14)

I am trying to design a DFA s.t. The set of strings in x ∈ {0, 1}∗
such that the number of zeros is a multiple of 3 and the number of one's is even.

My idea was to create two Machines M1 = (Q1, Σ, δ1, q1, F1), M2 = (Q2, Σ, δ2, q2, F2).

The first M checks if the number of 1's is even, and the second checks if the number of zeros is a multiple of 3.

If M1 accepts and M2 accepts, that is M1 intersection M2, then M accepts the input A. Is this a valid representation of a possible DFA, or am I supposed to make a singular Machine M s.t. the DFA accepts the input A?

**Tags:** automata-theory, dfa

> **Comments:**
> **username_1**: You should try using the Cartesian product construction.  It will allow you to build a new automaton based on M1 and M2's state diagrams.  :)  
> **username_2**: In the future, please try [CS Stackexchange](https://cs.stackexchange.com/) for these non-research-level questions.  

---

## 1 answers

### Answer by username_0 on 2018-01-14. Score: 1

Thanks to the hint given by @Micheal Wehar, I looked into Cartesian Product constructions and Intersections and I came across this answer:

<https://stackoverflow.com/questions/7780521/how-to-use-the-intersection-construction-to-form-a-dfa>

which seems to answer the question appropriately.

> **Comments:**
> **username_2**: In the future, please try [CS Stackexchange](https://cs.stackexchange.com/) for these non-research-level questions.  

---

