Year: 1997
Type: conference-paper
Abstract: We prove that the Berman-Hartmanis isomorphism conjecturers true under ACO reductions.More generafly, we show three theorems that hold for any comdexitv class C closed under (uniform) TCO-commtable man~-one" reductions.Isomorp'hism:The sets c~mplete for Cunder ACO reductions are afl isomorphic under isomorphisms computable and invertible by ACO circuits of depth three.Ga : p The sets that are complete for C under ACO and NC reducibility coincide.Stop Gap: The sets that are complete for C under ACO[mod 2] and ACO reducibility do not coincide.(These theorems hold both in the non-uniform and P-uniform settings.) To prove the second theorem for P-uniform settings, we show how to derandomize a version of the switching lemma, which may be of independent interest.(We have recently learned that this result is originally due to Ajtai and Wigderson, but it has not been published.)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2114377582