Machine one Construct a Turing Machine (all on paper, no programming/source code needed) that computes the function f(n) = n mod 3 In other words, for you non-math majors: sd It will halt successfully if the number is divisible by 3. 11 (good) 1001 (good) 1101 (bad) It will go to a reject state with bad input. There's a pattern you can figure out to set up your states. Machine two Construct a machine that accepts if the input string {S = x^n y^n } and rejects anything else. In other words it accepts if there are a certain number of x's followed by the same amount of y's. xx (bad) xxyy (good) xxxyyyy (bad) xxxxxyyyyy (good) You can write other symbols if you would like, but the only accept strings are x's followed by same amount of y's.