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Find out the Regular expression for the given finite automata
Problem
Construct a regular expression for the given finite automata.
Solution
Step 1 − Let us write down the equation.
q1=q1a+ ε
q1 is the start state and ε will be added as the input a which is coming to q1 from q1.
Hence, we write
State=source state of input * input coming to it
Step 2 − Similarly,
q2=q1b+q2b
q3=q2a
Step 3 − Let us simplify q1 first.
q1=q1a+ ε
we can re-write it as follows−
q1= ε +q1a
Which is similar to R=Q+RP which has a solution as follows−
R=QP*
Step 4 − Assuming R=q1, Q= ε, P=a
We get q1 = ε.a* since ε.R=R
q1=a*
Step 5 − Substituting values of q1 in q2 we get,
q2= q1a+q2b
=a*b+q2b
Step 6 − We compare this equation with R=Q+RP
Assuming R=q2, Q=a*b, P=b
We get, q2=a*b.b* as RR*=R+
We will get q2=a*.b+
Step 7 − From the given finite automata, if we want to find out the regular expression, we normally calculate the equation for the final state.
Since in the given finite automata, q2 is a final state and q2=a*b+
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