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is there any hierarchy for many-one complete languages of re (re-complete languages)? how can we propose a categorization for these languages? depending on what measures?

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using a weaker reduction. – Kaveh Feb 13 '12 at 1:43

Under many-one reductions by arbitrary total computable functions, HALT is the prototypical re-complete problem. A common technique for showing that some problem is undecidable (though not usually expressed in these terms) is to show that it is re-hard by reduction from HALT.

Using a weaker class of allowed reductions may lead to fewer problems being complete, but HALT is still re-complete even under linear-time many-one reductions.

For some reason, this terminology is much less used (to the point of not being used at all) in computability than in complexity.

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