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Revision difference : non-deterministic Turing machine |
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| 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. |
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. |
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If $S\in\Gamma^+$ 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 $S$.
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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 $F$.
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An alternative definition of a non-deterministic Turing machine is as a deterministic Turing machine with an extra 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 \emph{certificate} for $S$, and otherwise that it rejects $S$.
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An alternative definition of a non-deterministic Turing machine is as a deterministic Turing machine with an extra 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 \emph{certificate} for $S$ $S$.
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