MHB Answer: Language of Automata: DFA Q1, Q2

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The discussion centers on identifying the language accepted by a given DFA with states Q1, Q2, and Q3, where Q1 and Q2 are final states. The initial inquiry seeks the language representation as a regular expression. Participants clarify that starting from Q1, valid words can be expressed as b*a*, while starting from Q2 only allows for a*. The conversation reveals confusion regarding transitions to state Q3, which is non-final and complicates the DFA's determinism. Ultimately, it is suggested that state Q3 should be removed to simplify the state machine and ensure it is deterministic.
mathmari
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Hi! Could you help me finding the language that is accepted by the DFA with the following state diagram?

___| a ____ b
Q1 | Q2 __ Q1
Q2 | Q2 __ Q3
Q3 | Q3 __ Q3

final states: Q1, Q2
 
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mathmari said:
Hi! Could you help me finding the language that is accepted by the DFA with the following state diagram?

___| a ____ b
Q1 | Q2 __ Q1
Q2 | Q2 __ Q3
Q3 | Q3 __ Q3

final states: Q1, Q2

Hi mathmari!

What is your start state?

If Q3 is not a final state, you can never go to Q3, since you can never go back.
Is that what you intended?

How do you want your language?
As a regular expression?
In BNF syntax? Or EBNF?

If you start in state Q1, the words you can form are $b*a*$, where $*$ denotes zero or more.
Starting from state Q2, you can only form $a*$, which is already included.
 
I like Serena said:
Hi mathmari!

What is your start state?

If Q3 is not a final state, you can never go to Q3, since you can never go back.
Is that what you intended?

How do you want your language?
As a regular expression?
In BNF syntax? Or EBNF?

If you start in state Q1, the words you can form are $b*a*$, where $*$ denotes zero or more.
Starting from state Q2, you can only form $a*$, which is already included.

The start state is Q1.
I want the language as a regular expression.
 
mathmari said:
The start state is Q1.
I want the language as a regular expression.

Then I guess I've already answered your question...
 
I like Serena said:
If you start in state Q1, the words you can form are $b*a*$, where $*$ denotes zero or more.

Starting in state Q1, couldn't the words be also $ a*b*$ ?
 
mathmari said:
Starting in state Q1, couldn't the words be also $ a*b*$ ?

After you accept the first $a$, accepting a $b$ would bring you to state Q3.
And from state Q3 you can never get to a final state anymore.

It is a bit weird though that you would have a state that doesn't go anywhere.
Are you sure that is right?
 
I like Serena said:
After you accept the first $a$, accepting a $b$ would bring you to state Q3.
And from state Q3 you can never get to a final state anymore.

It is a bit weird though that you would have a state that doesn't go anywhere.
Are you sure that is right?

Now I looked at the exercise again and realized that the state Q2 with $b$ goes to the state Q1 and to the state Q3.
 
mathmari said:
Now I looked at the exercise again and realized that the state Q2 with $b$ goes to the state Q1 and to the state Q3.

So your transition table is incomplete?
But still no other transitions starting from state Q3?
 
I like Serena said:
So your transition table is incomplete?
But still no other transitions starting from state Q3?

Starting from Q3 with $a$ or $b$ it goes to the state Q3 again...
 
  • #10
How can the state Q2 go with b to the state Q1 and also to the state Q3? :confused:
 
  • #11
mathmari said:
How can the state Q2 go with b to the state Q1 and also to the state Q3? :confused:

Now that you mention it, that's not really deterministic is it?
However, if it would go to state Q3, it can never reach a final state anymore.

In my opinion, your state machine is screwed up.
State Q3 should be deleted altogether, including all transitions toward it.
Then we're left with a nice and deterministic state machine. ;)
 
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