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sav08:using_automata_to_decide_ws1s [2012/05/15 12:46] vkuncak |
sav08:using_automata_to_decide_ws1s [2012/05/15 15:11] vkuncak |
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| - | Instead of $e(F)(D,\alpha(w))={\it true}$ we write for short $w \models F$. | + | Instead of $e(F)(D,\alpha(w))={\it true}$ we write for short $w \models F$. So, we design automata so that: |
| + | \[ | ||
| + | w \in L(A(F)) \ \ \ \iff \ \ \ w \models F | ||
| + | \] | ||
| The following lemma follows from the definition of semantic evaluation function 'e' and the shorthand $w \models F$. | The following lemma follows from the definition of semantic evaluation function 'e' and the shorthand $w \models F$. | ||
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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 interpreted 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. Also compute the automaton for the formula $\exists X. (X < Y)$. |
| ===== References ===== | ===== References ===== | ||