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Every nontrivial property of the recursively enumerable languages is undecidable.

What exactly is nontrivial property?

Ran G.
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Alvar
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1 Answers1

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A property that holds for every machine or holds for none is trivial. Rice's theorem does not apply to such a property.

To see why, note that such a property can be decided by a very simple Turing machine, which accepts/rejects every Turing machine representation.

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