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 −

Step 3

Divide tables into 2 tables as shown below −

Table 1 starts from the non-final states.

Table 2 starts from the final states.

Step 4

Remove similar rows.

Table 1 has no similar rows

Table 2 has similar rows. So, skip q5 and replace q5 by q3

Step 5

Combine two tables as shown below −

Thus, the minimized DFA will be as follows −

Bhanu Priya

Updated on: 12-Jun-2021

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