Questions tagged [rice-theorem]

Rice's Theorem states that any (non-trivial) property of Turing machines is undecidable.

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Determine if a language is Decidable or semi decidable

Consider the language $L = \{\langle M \rangle: \text{$M$accepts at most two single-letter words}\}$, where $\langle M\rangle$ is the encoding of Turing machine $M$. We need to determine, without ...
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Is my assumption about non trivial propery correct?

"make sure you understand why for a non trivial property $S$, $\bar{S}$ is also non trivial" My assumption is: $S$ is non trivial property: There are L1,L2 such that $L_{1},L_{2}\in RE$ and ...
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Using Rice's theorem to prove undecidability of $E_{TM}$

I saw this proof and I wondered if I could prove $E_{TM}$ with Rice's theorem similar to the one described in the answer. Can you do the same thing by letting $M$ to only accept empty strings? (the $M$...
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Is undecidability of TMs' properties a statistical statement?

We know (by Rice's theorem) that is it not possible to decide a non-trivial property of a given TM. We could say therefore that we cannot be sure at 100 percent that a given TM has a certain non-...
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Show that $L = L_\phi \cup L_{\{\sum^*\}} \notin RE$ with Rice theorem
Show that $L = L_\phi \cup L_{\{\sum^*\}} \notin RE$ with Rice theorem. Well I did show that with reduction, by using $HP'$. Simply by creating a function from $f(\langle M \rangle, x) = (M')$ Thus, ...