A Turing machine is an idealization of a computing machine.
The idea goes as follows.
To simplify things, the piece of paper being worked on is in the form of a series of boxes on a one-dimensional "tape" divided into squares.
The machine examines one square at a time, and carries out an action determined by both:
- $(1): \quad$ the symbol in the square
- $(2): \quad$ the current internal state of the machine.
The internal state of the machine is a way of providing a device that can keep track of the symbols in other squares.
There can be only a finite set of these states, say $q_1, q_2, \ldots, q_\beta$.
The actions that the machine can take are as follows:
- $(1): \quad$ Replace the symbol in the square with another symbol
- $(2): \quad$ Move to examine the square in the immediate left of the current square being looked at
- $(3): \quad$ Move to examine the square in the immediate right of the current square being looked at.
After carrying out an action, the machine may change to a different internal state.
The program for the machine is a set of instructions which specify:
- $(1): \quad$ what action to take in some possible combinations of the internal state and symbol in the square currently being read
- $(2): \quad$ which internal state the machine moves into after carrying out that action.
Thus the instructions have the following form:
- $q_i \quad s_j \quad A \quad q_t$
which is interpreted as:
- the machine is in internal state $q_i$
- the symbol in the square currently being examined is $s_j$
- Carry out action $A$
- Move into internal state $q_t$.
The actions can be abbreviated to:
- $L$: Move one square to the left
- $R$: Move one square to the right
- $s_k$: Replace the symbol in the square currently being read with symbol $s_k$.
The computation stops when there is no instruction which specifies what should be done in the current combination of internal state and symbol being read.
Also known as
Such a machine is also known as a deterministic Turing machine to distinguish it from the nondeterministic version.
- Results about Turing machines can be found here.
Source of Name
This entry was named for Alan Mathison Turing.