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- W2163247256 abstract "We show that all sets complete for NC/sup 1/ under AC/sup 0/ reductions are isomorphic under AC/sup 0/-computable isomorphisms. Although our proof does not generalize directly to other complexity classes, we do show that, for all complexity classes C closed under NC/sup 1/-computable many-one reductions, the sets complete for C under NC/sup 0/ reductions are all isomorphic under AC/sup 0/-computable isomorphisms. Our result showing that the complete degree for NC/sup 1/ collapses to an isomorphism type follows from a theorem showing that in NC/sup 1/, the complete degrees for AC/sup 0/ and NC/sup 0/ reducibility coincide. This theorem does not hold for strongly uniform reduction: we show that there are Dlogtime-uniform AC/sup 0/-complete sets for NC/sup 1/ that are not Dlogtime-uniform NC/sup 0/-complete." @default.
- W2163247256 created "2016-06-24" @default.
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- W2163247256 date "2002-12-23" @default.
- W2163247256 modified "2023-09-28" @default.
- W2163247256 title "An isomorphism theorem for circuit complexity" @default.
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- W2163247256 doi "https://doi.org/10.1109/ccc.1996.507663" @default.
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