Question

If M is a nondeterministic finite automaton, then there is a deterministic

finite automaton equivalent to M.

Answer 1

The process of subset construction allows for the creation of a deterministic finite automaton equivalent to a nondeterministic finite automaton.

Step-by-step explanation:

When considering a nondeterministic finite automaton (NFA), there is a way to construct an equivalent deterministic finite automaton (DFA) that represents the same language. This process is known as subset construction. Here are the steps to create a DFA equivalent to an NFA:

1. Create an initial state that represents the set of NFA states reachable from the start state by taking the epsilon transitions.
2. For each input symbol, find the set of NFA states reachable from the current DFA state by taking that input symbol's transitions.
3. Repeat step 2 for each input symbol until no new states are created.
4. The resulting states of the DFA represent subsets of the states of the NFA.
5. The final states of the DFA are the subsets of NFA states containing at least one final state.

This process ensures that the DFA and NFA recognize the same language. So, if M is an NFA, there is a DFA equivalent to M.