Reductions in Circuit Complexity : An Isomorphism Theorem and a Gap Theorem . 1
نویسندگان
چکیده
We show that all sets that are complete for NP under non-uniform AC0 reductions are isomorphic under non-uniform AC0-computable isomorphisms. Furthermore, these sets remain NP-complete even under non-uniform NC0 reductions. More generally, we show two theorems that hold for any complexity class C closed under (uniform) NC1-computable many-one reductions. Gap: The sets that are complete for C under AC0 and NC0 reducibility coincide. Isomorphism: The sets complete for C under AC0 reductions are all isomorphic under isomorphisms computable and invertible by AC0 circuits of depth three. Our Gap Theorem does not hold for strongly uniform reductions: we show that there are Dlogtime-uniform AC0-complete sets for NC1 that are not Dlogtime-uniform NC0-complete.
منابع مشابه
Reductions in Circuit Complexity: An Isomorphism Theorem and a Gap Theorem
We show that all sets that are complete for NP under non-uniform AC reductions are isomorphic under non-uniform AC-computable isomorphisms. Furthermore, these sets remain NP-complete even under non-uniform NC reductions. More generally, we show two theorems that hold for any complexity class C closed under (uniform) NC-computable many-one reductions. Gap: The sets that are complete for C under ...
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