Summary: Reductions in Circuit Complexity:
An Isomorphism Theorem and a Gap Theorem.
Manindra Agrawal Eric Allendery
Department of Computer Science Department of Computer Science
Indian Institute of Technology Rutgers University
Kanpur 208016 P.O. Box 1179
India Piscataway, NJ 08855-1179
Computer Science Department
Carnegie Mellon University
Pittsburgh, PA 15213
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 un-