Consider the function defined by f(n) = 2 nwhere n is a positive integer. (i) Can...
Consider the function defined by f(n) = 2 nwhere n is a positive integer.
(i) Can this function be computed by a Turing machine? Why or why not?
(ii) Is this function primitive recursive? Why or why not?
Homework Answers
1. The idea behind a turing machine is that it can simulate ANY computer algorithm, no matter how complicated it is. A turing machine can perform any computation which is capable of being performed by a modern day computer. Since the above function can be easily computed by a modern computer it can be computed by a turing machine as well.
2. A primitive recursive function a function that can be computed by a program whose loops are all "for" loops. The upper bound for the iterations of the loop is pre determined. The function can be written using a for loop, by adding the value of n to a sum variable initialised to 0 and running it 2 times. Hence it is a primitive recursive function.
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