# Difference between Turing machine end state and halt

Is there a difference between the end state of a Turing machine and the halt state? Especially, for example the Busy Beaver 3. It is said that it is with 3 states but there is also a halt. Is the end state $q_2$ or the $halt$?

• Busy Beaver is a famous Turing machine problem, which aims of determining the maximum number of steps, done by a TM, when computing the number of 1s starting from an empty tape. For one 1 (one state) - one step, for four 1s (2 states) - six steps, for six 1s (3 states) - fourteen steps. So it grows exponentially. Therefore, it is proved that it`s not computable. The problem however, dates back from 1960s. Commented Jan 28, 2015 at 20:13
• The growth is not exponential, it is super-exponential. Also, exponential growth (and even super-exponential growth) doesn't imply non-computable. However it happens to be the case that the busy beaver function growths faster than every computable function. Commented Feb 22, 2015 at 22:04

• Also, considering the definition of the busy beaver problem, the halting state is not considered a "regular" state, probably because it is not optional. I believe you are making the common mistake of thinking that the state with the higher index ($q_2$, in your example) has some special attribute, but it doesn't. Commented Apr 24, 2015 at 4:05