NFA to DFA (Nondeterministic Finite Automaton to Deterministic Finite Automaton) conversion involves transforming a nondeterministic automaton into an equivalent deterministic automaton. The process is known as the subset construction and follows these steps:
Initial State:
- The initial state of the DFA is the ε-closure of the initial state of the NFA. It represents the set of states that can be reached from the NFA's initial state using ε-transitions.
Transition Function:
- For each state set in the DFA and for each input symbol:
- Determine the set of states that can be reached from the current set through transitions on the input symbol.
- This set is the ε-closure of the union of states reached by the NFA's transition function.
Final States:
- A state set in the DFA is a final state if it contains at least one final state of the NFA.
The resulting DFA, obtained through this conversion, recognizes the same language as the original NFA. The power set construction or subset construction systematically explores the possible combinations of states in the NFA, effectively simulating the nondeterministic behavior of the original automaton in a deterministic way.