In addition, the machine has a register, which records the state of the machine (one of a finite number of states), and a table of rules. The Turing machine is useful because it is possible to charact...In addition, the machine has a register, which records the state of the machine (one of a finite number of states), and a table of rules. The Turing machine is useful because it is possible to characterize the set of functions that can be computed by a Turing machine, which is what Turing did. It turns out that just about every reasonable model of computation anyone has come up with is “Turing complete"; that is, it can compute exactly the same set of functions as the Turing machine.
