COT 5310: Assignment 4
1.
Present a Turing Machine to do MAX of n non-zero arguments, n>=0. You
know you’ve run out of arguments when you encounter the value 0, represented
by two successive 0's (blanks). Use the machines we have already built up and
others you build. Do
NOT
turn in Turing Tables. We won't pay any attention to
them if you do.
2.
Show that Turing Machines are closed under primitive recursion. This
completes the equivalence proofs for our five models of computation.
To prove the that Turing Machines are closed under primitive recursion, we must
simulate some arbitrary primitive recursive function F(x
1
,x
2
, …, x
n
,y) on a Turing
Machine. To show this, we define F(x
1
,x
2
, …, x
n
,y) recursively as:
F(0, x
1
,x
2
, …, x
n
) = G(x
1
,x
2
, …, x
n
)
F(y+1, x
1
,x
2
, …, x
n
) = H(y, x, F(y,x
1
,x
2
, …, x
n
))
Where, G and H are Standard Turing Computable. We define the function F for the
Turing Machine as the following:
Since our Turing Machine simulator can produce the same value for any arbitrary PRF, F,