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1-  Consider a TM tape containing a number in unary form (i.e., the number n is represented by a string of n 1’s).

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Give a Turing machine that computes the function f(x) = x % 3 (i.e., that replaces the input number on the tape by its remainder when divided by 3.

Below, give a simple summary of the inputs associated with each state in your TM controller.


2- Give a Turing machine that accepts the set of strings over {0.1} havng the form 0i1j with i ≠ j.

Below, give a simple summary of the inputs associated with each state in your TM controller.



Describe the function computed by the following Turing machine. Assume the tape contains an input number in unary form (i.e., we represent the number n by a string of n 1’s).

for q3 I uploaded the picture