# Finite automata start state

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.

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

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 $$\emptyset$$.