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aa:lab:rice [2016/10/22 11:23] pdmatei created |
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| ==== Establish the hardness of the following ==== | ==== Establish the hardness of the following ==== | ||
| + | {{## | ||
| * $math[f(M_1,M_2) = \left\{\begin{array}{ll} 1 & M_1 \text{ takes as much time as } M_2 \text{ on every input } \\ 0 & \text{otherwise} \end{array}\right.] | * $math[f(M_1,M_2) = \left\{\begin{array}{ll} 1 & M_1 \text{ takes as much time as } M_2 \text{ on every input } \\ 0 & \text{otherwise} \end{array}\right.] | ||
| + | ##}} | ||
| + | * $math[f(M) = \left\{\begin{array}{ll} 1 & M \text{ does not terminate for every input } \\ 0 & \text{otherwise} \end{array}\right.] | ||
| + | |||
| + | ==== Reading Rice's Theorem ==== | ||
| + | |||
| + | $prop[Rice] | ||
| + | Let $math[\mathcal{C} \subseteq RE]. Given a Turing Machine $math[M], we ask:// "The problem accepted by $math[M] is in $math[\mathcal{C}]?". //Answering this question is not in $math[R] (not decidable). | ||
| + | $end | ||
| + | |||
| + | * Rice's theorem establishes undecidability of a problem. Which problem is that? | ||
| + | * What does this result entail? | ||
| + | * Examine the transformation from the lecture, and prove both directions by yourself. | ||