deterministic Turing machine

The formal definition of a deterministic Turing machine is a tuple:


Where Q is a finite setMathworldPlanetmath of states, Γ is the finite set of tape symbols, BΓ is the blank symbol, ΣΓ is the set of input symbols, δ:Q×ΓQ×Γ×{L,R} is the move function, q0Q is the start state and FQ is the set of final states. (Note that, despite the name, δ is a partial functionMathworldPlanetmath which will be undefined for some pairs (q,A).)

A Turing machineMathworldPlanetmath is conceived to be a box with a tape and a tape head. The tape consists of an infiniteMathworldPlanetmath number of cells stretching in both directions, with the tape head always located over exactly one of these cells. Each cell has symbol from Γ written on it.

At the beginning of its computation, T is in state q0 and a finite string S (the input string) over the alphabet Σ is written on the tape, with the tape located over the first letter of S. Each cell before the beginning or after the end of S is blank. For each move, if the current state is q and the value of the cell under the tape head is A then suppose δ(q,A)=(q,A,D). The value of the cell under the tape head is changed to A, the state changes to q, and the tape head moves to the left if D=L and to the right if D=R. If δ(q,A) is undefined then the machine halts.

For any SΓ+, we say T accepts S if T halts in a state qF when S is the input string, that T rejects S if T halts in a state qF, and otherwise that T does not halt on S.

This definition can easily be extended to multiple tapes with various rules. δ should be a function from Q×ΓnΓm×{L,R}n where n is the number of tapes, m is the number of input tapes, and L is interpreted to mean not moving (rather than moving to the left) for one-way tapes.

Title deterministic Turing machine
Canonical name DeterministicTuringMachine
Date of creation 2013-03-22 13:01:22
Last modified on 2013-03-22 13:01:22
Owner Henry (455)
Last modified by Henry (455)
Numerical id 8
Author Henry (455)
Entry type Definition
Classification msc 68Q05
Classification msc 68Q10
Related topic TuringMachine2