non-deterministic Turing machine

The definition of a non-deterministic Turing machine is the same as the definition of a deterministic Turing machine except that δ is a relationMathworldPlanetmath, not a function. Hence, for any particular state and symbol, there may be multiple possible legal moves.

If SΓ+ we say T accepts S if, when S is the input, there is some finite sequencePlanetmathPlanetmath of legal moves such that δ is undefined on the state and symbol pair which results from the last move in the sequence and such that the final state is an element of F. If T does not accept S then it rejects S.

An alternative definition of a non-deterministic Turing machine is as a deterministic Turing machine with an extra one-way, read-only tape, the guess tape. Then we say T accepts S if there is any string c(S) such that, when c(S) is placed on the guess tape, T accepts S. We call c(S) a certificate for S, and otherwise that it rejects S. In some cases the guess tape is allowed to be two-way; this generates different time and space complexity classesPlanetmathPlanetmath than the one-way case (the one-way case is equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath to the original definition).

Title non-deterministic Turing machine
Canonical name NondeterministicTuringMachine
Date of creation 2013-03-22 13:01:25
Last modified on 2013-03-22 13:01:25
Owner Henry (455)
Last modified by Henry (455)
Numerical id 6
Author Henry (455)
Entry type Definition
Classification msc 68Q05
Related topic TuringMachine2
Defines certificate