使用图灵机指定给定序列的成员

Question

我遇到的一个问题是，给定二进制序列a_0，...，a_ {n-1}需要多少转换，以便当给定非负整数i时，如果i

使用https://martinugarte.com/turingmachine/我模拟了以下图灵机，试着了解应该采取多少个状态

n = 2,5转换的序列

//Sequence is 0,1
name: Sequence
init: one
accept: end

one,0
end,0,-

one,1
two,_,>

two,_
end,1,-

two,0
end,0,-

two,1
end,0,-

用n = 3，8个转换序列

//Sequence is 0,1,0
name: Sequence
init: one
accept: end

one,0
end,0,-

one,1
two,_,>

two,_
end,1,-

two,0
three,_,>

two,1
end,0,-

three,_
end,0,-

three,0
end,0,-

three,1
end,0,-

n = 4,11次转换的序列

//Sequence is 0,1,0,1
name: Sequence
init: one
accept: end

one,0
end,0,-

one,1
two,_,>

two,_
end,1,-

two,0
three0,_,>

two,1
three1,_,>

three0,_
end,0,-

three0,0
end,0,-

three0,1
end,0,-

three1,_
end,1,-

three1,0
end,0,-

three1,1
end,0,-

由此我猜测，指定序列n long需要大致O（n）个状态。你能证明这一点吗？