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sav08:using_automata_to_decide_ws1s [2011/04/12 15:08] vkuncak |
sav08:using_automata_to_decide_ws1s [2012/05/15 12:46] vkuncak |
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| **Lemma**: Let $F,F_i$ denote formulas, $w \in \Sigma^*$. Then | **Lemma**: Let $F,F_i$ denote formulas, $w \in \Sigma^*$. Then | ||
| - | * $w \models (F_1 \lor F_2)$ iff $w \models F_1$ and $w \models F_2$ | + | * $w \models (F_1 \lor F_2)$ iff $w \models F_1$ or $w \models F_2$ |
| * $w \models \lnot F$ iff $\lnot (w \models F)$ | * $w \models \lnot F$ iff $\lnot (w \models F)$ | ||
| * $w \models \exists x.F$ iff $\exists b. patch(w,x,b) \models F$ | * $w \models \exists x.F$ iff $\exists b. patch(w,x,b) \models F$ | ||
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| **Example 1:** Compute automaton for formula $\exists X. \lnot (X \subseteq Y)$. | **Example 1:** Compute automaton for formula $\exists X. \lnot (X \subseteq Y)$. | ||
| - | **Example 2:** Compute automaton for formula $\exists Y. (X < Y)$ where $<$ is interepretted treating $X,Y$ as digits of natural numbers. | + | **Example 2:** Compute automaton for formula $\exists Y. (X < Y)$ where $<$ is interpreted treating $X,Y$ as digits of natural numbers. |
| ===== References ===== | ===== References ===== | ||