Question

I need help designing a turing machine that will compute the following f(x) = x mod 3. I just need help getting started since I am not familiar on how to approach this problem

Answer 1

Extracts from the comments:

The input and input is in unary as a string of 1. Space is 0. The output should rewrite the input.

The input is {x, 3} with one space between each argument or {x}.

The output is {x mod 3}.

Algorithm:

• Go to the end of the input.
• Remove the second argument.
• While there are at least three symbols in the argument, remove them.

State machine:

• Start: If input is 0, move right and go to “deleting right”, else move right.
• Deleting right: If input is 0, move left and go to “finding arg”. Else write 0 and move right.
• Finding arg: If input is 0, move left. If input is “start of tape”, finish. Else move left and go to state “found 1”.
• Found 1: If input is “start of tape”, finish. Else move left and go to the state “found 2”
• Found 2: If input is “start of tape”, finish. Else and go to the state “deleting right”.