00:03
We're asked to construct a touring machine that computes the function f of n equals 3 times n plus 2, which is the same as 3n plus 6.
00:10
By finding the composite of the touring machines we constructed in previous exercises.
00:17
So notice that our function f is actually the composite g circle h, where g of n is 3n for all non -negative integers n, and h of n is n plus 2 for all non -negative integers n.
00:42
And we have constructed touring machines for both of these.
00:47
So for gm, we constructed a touring machine i'll call t1.
01:00
And for hn, we constructed a turing machine, which i'll call t2.
01:05
Now to find a turing machine which models f, this is going to be the composite touring machine, t1, t2.
01:17
And we have by the definition of the composite turing machine.
01:31
This is going to be a turing machine which contains, well, the set of states s is going to be a set of states from t1 and the set of states of t2 together.
01:55
Now, recall in making the turing machine for g of n equals 3n.
02:09
We saw that eight different states were required.
02:32
So i've actually got this backwards here.
02:35
First we want to compute.
02:49
We want to compute h of n.
02:54
So this should actually be t1 instead of g of n.
03:01
And then g of n as training machine t2...
