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sav07_homework_1_solution [2007/03/17 18:58] vkuncak |
sav07_homework_1_solution [2007/03/17 19:00] vkuncak |
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| a precondition and 2) that if we take any other precondition, it will be a subset of | a precondition and 2) that if we take any other precondition, it will be a subset of | ||
| wp. | wp. | ||
| + | |||
| ==== Task 5 ==== | ==== Task 5 ==== | ||
| Line 79: | Line 80: | ||
| </latex> | </latex> | ||
| - | does not hold in general. | + | does not hold in general. As a counterexample, take three |
| + | distinct states s_1, s_2, and s_3, and let | ||
| + | |||
| + | <latex> | ||
| + | \begin{array}{l} | ||
| + | r = \{ (s_1,s_2), (s_1,s_3) \} \\ | ||
| + | Q_1 = \{ s_2 \} \\ | ||
| + | Q_2 = \{ s_3 \} | ||
| + | \end{array} | ||
| + | </latex> | ||
| Note: the property does hold for deterministic relations. | Note: the property does hold for deterministic relations. | ||