# 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 $\delta $ is a relation^{}, not a function. Hence, for any particular state and symbol, there may be multiple possible legal moves.

If $S\in {\mathrm{\Gamma}}^{+}$ we say $T$ accepts $S$ if, when $S$ is the input, there is some finite sequence^{} of legal moves such that $\delta $ 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 classes^{} than the one-way case (the one-way case is equivalent^{} 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 |