Explain with an example how to convert NFA to DFA.

Data Structure AlgorithmsComputer ScienceComputers


Convert the following Non-Deterministic Finite Automata (NFA) to Deterministic Finite Automata (DFA).


The transition diagram is as follows −

The transition table of NFA is as follows −


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 −


In the above transition table, q2 is the final state. Wherever, q2 is present that becomes the final state.


  • 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 09:17:08