Question

Create a turing machine for the following functions

f(x) = 2x

Answer 1

Turing machine for f(x) = 2x
A function f is turing computable if and only if ther exists some turing machine such that f(x) = y

• if there exists some final state af such that 90 * afy halts.
• now construct turing machine that computes f(x) = 2x, where x is positive integer that represented with unary notation as start with 111 and end with 111 111

f(x) = 2x in unary notation; double the length of contiguous it currently being scanned by read write head

• Initial:- 011110, the read write scans the right most 1's of a string oc contiguous.
• Intermediate:- 0110 1100. there a two strings of continuous 1's separate by a single 0. 1's have been deleted at left, twice that number have been written at right.
• next step:- 0110 11110... the new string has been extend by 1 at each end.
• final:- 0111111110.. string af is erased, a new string twice as long has been created