Can a finite automata not have a start state?

I think it is possible for a finite automata to not have a start state. However, I'm not sure if I'm correct.

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    $\begingroup$ What does the definition say? Overall, it's not important. You can simply say that automaton without starting state accepts an empty language. $\endgroup$
    – user114966
    Mar 28, 2021 at 19:16

1 Answer 1


It depends on the definition. Some definitions of a deterministic finite automaton (DFA) are a quadruplet $(Q, \delta, q_0, F)$ where $Q$ is the set of states and $q_0 \in Q$ is the initial state. Therefore, it must be defined.

However, the definition of non-deterministic finite automaton (NFA) is sometimes seen as a quadruplet $(Q, \Delta, I, F)$ where $Q$ is the set of states and $I\subset Q$ is the set of initial states. Here, you can chose $I = \emptyset$ and get an automaton without initial state.

Since a DFA can be seen as a special case of a NFA, it is not necessary for an automaton to have an initial state. In both cases (DFA and NFA), the language recognized by an automaton without initial state is $\emptyset$.


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