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sav08:logic_and_automata_introduction [2008/05/14 10:14] vkuncak |
sav08:logic_and_automata_introduction [2015/04/21 17:30] (current) |
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| Compute the unary relation (set) corresponding to this formula $F(z)$: | Compute the unary relation (set) corresponding to this formula $F(z)$: | ||
| - | \[ | + | \begin{equation*} |
| \exists x. \exists y.\ z = 2 x + 1 \land z = 3 y + 2 | \exists x. \exists y.\ z = 2 x + 1 \land z = 3 y + 2 | ||
| - | \] | + | \end{equation*} |
| ++++| | ++++| | ||
| Add 6k to solution, we obtain a solution. \\ | Add 6k to solution, we obtain a solution. \\ | ||
| Line 25: | Line 25: | ||
| Find solutions in set $\{0,1,2,3,4,5\}$. \\ | Find solutions in set $\{0,1,2,3,4,5\}$. \\ | ||
| - | Resulting relation for $F(z)$ is $\{ 6k + 5 \mid k \in \mathbb{Z} \}$. | + | Resulting relation for $F(z)$ is $\{ 6k + 5 \mid k \in \mathbb{N} \}$. \\ |
| + | |||
| + | Representation as quantifier-free formula. \\ | ||
| + | |||
| + | Representation as a regular language. | ||
| ++++ | ++++ | ||