Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | |||
|
aa:lab:decidability [2016/10/16 19:49] dalex formatting |
aa:lab:decidability [2016/11/01 12:07] (current) pdmatei |
||
|---|---|---|---|
| Line 2: | Line 2: | ||
| We recall a few basic definitions. Let $math[M] be a Turing Machine over $\Sigma^*$ and $math[f:\Sigma^*\rightarrow\{0,1\}] be a decision problem. Then: | We recall a few basic definitions. Let $math[M] be a Turing Machine over $\Sigma^*$ and $math[f:\Sigma^*\rightarrow\{0,1\}] be a decision problem. Then: | ||
| - | * $math[M] accepts $math[f] $math[\iff] $math[\forall w\in\Sigma^*: M(w) = 1 \iff f(w) = 1] | + | * $math[M] accepts $math[f] $math[\iff] $math[\forall w\in\Sigma^*: M(w) = 1 \iff f(w) = 1] and $math[M(w) = \bot \text{ otherwise }] |
| * $math[M] decides $math[f] $math[\iff] $math[M] accepts $math[f] and $math[M] halts for all inputs. | * $math[M] decides $math[f] $math[\iff] $math[M] accepts $math[f] and $math[M] halts for all inputs. | ||