Construct NFA without ∈ transitions
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| NFA with ∈ |
Sol.
Step 01: Find ∈-closure of (q1), (q2) and (q3).
∈-closure of (q1) = {q1, q2, q3}
∈-closure of (q2) = {q2, q3}
∈-closure of (q3) = {q3}
For each state find the next state for each input. See the table below,
|
State |
0 |
1 |
2 |
|
->q1 |
{q1,q2,q3} |
{q2,q3} |
{q3} |
|
q2 |
φ |
{q2,q3} |
{q3} |
|
q3 |
φ |
φ |
{q3} |
From the question diagram, it is clear that only with ∈ input q1 and q2 state can reach to the final state.
So, now without ∈ input, q1 and q2 is also treated as final states.
As shown in diagram below.
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| NFA without ∈ |