# Can a Turing Machine have infinite accept states?

I'm still fairly new to Turing Machines, but I've been doing some research.

I know that a Turing Machine can have an infinite tape and that it requires a finite number of states, but does it necessarily follow that a Turing Machine can have an infinite number of accept states?

I keep seeing different layouts when formally defining Turing Machines, for example:

M = (Q, Σ, Γ, τ, s, F).

1) F ⊆ Q is the set of final or accepting states. (plural)

2) F ⊆ Q is the accept state. (singular)

So I'm just wondering which one is correct?

Any help would be greatly appreciated.

• Possible duplicate of Can a Turing machine have infinite states? Commented Nov 23, 2015 at 6:12
• You are talking about three different cases here: Turing machines with one accepting state, with several (a finite number of them) or infinite ones. Which ones do you mean? Commented Nov 23, 2015 at 12:26

In the standard Turing machine, the set of states $Q$ is finite $|Q| < \infty$. Therefore, it cannot have infinite final states. However, it may, or may not have multiple final states. This will not change the power of the machine (i.e., one final state is equivalent to $k$ final states).