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What is Minimization of DFA?
Problem
Given a Deterministic Finite Automata (DFA), try to reduce the DFA by removing unreachable states and removing similar rows.
Solution
Step 1
Remove the unreachable states from q0
From the initial states, we are not able to reach q2 and q4. So, remove these two states as shown below −
After removing unreachable states, the partial minimized DFA is as follows −
Step 2
The transition table is given below −
States | 0 | 1 |
---|---|---|
->q0 | q1 | q3 |
q1 | q0 | q3 |
*q3 | q5 | q5 |
*q5 | q5 | q5 |
Step 3
Divide tables into 2 tables as shown below −
Table 1 starts from the non-final states.
States | 0 | 1 |
---|---|---|
->q0 | q1 | q3 |
q1 | q0 | q3 |
Table 2 starts from the final states.
States | 0 | 1 |
---|---|---|
*q3 | q5 | q5 |
*q5 | q5 | q5 |
Step 4
Remove similar rows.
Table 1 has no similar rows
Table 2 has similar rows. So, skip q5 and replace q5 by q3
States | 0 | 1 |
---|---|---|
q3 | q5 | q3 |
Step 5
Combine two tables as shown below −
States | 0 | 1 |
---|---|---|
->q0 | q1 | q3 |
q1 | q0 | q3 |
*q3 | q3 | q3 |
Thus, the minimized DFA will be as follows −
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