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Explain with an example how to convert NFA to DFA.
Problem
Convert the following Non-Deterministic Finite Automata (NFA) to Deterministic Finite Automata (DFA).
Solution
The transition diagram is as follows −
The transition table of NFA is as follows −
| State | a | b |
|---|---|---|
| ->q0 | q0 | q0,q1 |
| q1 | - | *q2 |
| *q2 | - | - |
The DFA table cannot have multiple states. So, make q0q1 as a single state.
Let’s convert the given NFA to DFA by considering two states as a single state.
The transition table of DFA is as follows −
| State | a | b |
|---|---|---|
| ->q0 | q0 | [q0,q1] |
| [q0q1] | [q0] | [q0q1q2] |
| *[q0q1q2] | [q0] | [q0q1q2] |
In the above transition table, q2 is the final state. Wherever, q2 is present that becomes the final state.
Note −
- After conversion the number of states in the final DFA may or may not be the same as in NFA.
- The maximum number of states present in DFA may be 2pow (number of states in NFA)
- The relationship between number of states in NFA and DFA is: 1<=n<=2m
Where n= number of states in DFA
m= number of states in NFA
- The final DFA all states that contain the final states of NFA are treated as final states.
Updated on: 12-Jun-2021
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