Turing machine

A Turing machine has two components:

  • Central controller (where the states are)
    • A unique accepting state acc
    • A unique rejecting state rej
    • All other states are non-terminal(!), meaning that the Turing machine will continue running until either in state acc or rej
    • Each transition between states is in the form of , where is the direction, either R(right) or L(left). And are letters, is the current letter in the input line and is the letter to write into the input line.
  • Input line
    • The input line can be navigated both forward and backward
    • Input line spans infinitely both forward and backward, and all non-filled cells are considered to have a “space” character
    • It is possible to write into the input line(!)

Formal definition

Configuration

Turing machine language definition

Example

Example

Example

Example

Computing functions