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Automata Conversion of RE to FA

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Conversion of RE to FA

To convert the RE to FA, we are going to use a method called the subset method. This method is used to obtain FA from the given regular expression. This method is given below:

Step 1: Design a transition diagram for given regular expression, using NFA with ε moves.

Step 2: Convert this NFA with ε to NFA without ε.

Step 3: Convert the obtained NFA to equivalent DFA.

Example 1:

Design a FA from given regular expression 10 + (0 + 11)0* 1.

Solution: First we will construct the transition diagram for a given regular expression.

Step 1:

Conversion of RE to FA

Step 2:

Conversion of RE to FA

Step 3:

Conversion of RE to FA

Step 4:

Conversion of RE to FA

Step 5:

Conversion of RE to FA

Now we have got NFA without ε. Now we will convert it into required DFA for that, we will first write a transition table for this NFA.

State01
→q0q3{q1, q2}
q1qfϕ
q2ϕq3
q3q3qf
*qfϕϕ

The equivalent DFA will be:

State01
→[q0][q3][q1, q2]
[q1][qf]ϕ
[q2]ϕ[q3]
[q3][q3][qf]
[q1, q2][qf][qf]
*[qf]ϕϕ

Example 2:

Design a NFA from given regular expression 1 (1* 01* 01*)*.

Solution: The NFA for the given regular expression is as follows:

Step 1:

Conversion of RE to FA

Step 2:

Conversion of RE to FA

Step 3:

Conversion of RE to FA

Example 3:

Construct the FA for regular expression 0*1 + 10.

Solution:

We will first construct FA for R = 0*1 + 10 as follows:

Step 1:

Conversion of RE to FA

Step 2:

Conversion of RE to FA

Step 3:

Conversion of RE to FA

Step 4:

Conversion of RE to FA


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