A First-Order Isomorphism Theorem

We show that for most complexity classes of interest, all sets complete under rstorder projections (fops) are isomorphic under rst-order isomorphisms. That is, a very restricted version of the Berman-Hartmanis Conjecture holds. Since \natural" complete problems seem to stay complete via fops, this indicates that up to rst-order isomorphism there is only one \natural" complete problem for each \nice" complexity class.

• Type: Conference
• Year: 1993
• Where: STACS
• Authors: Eric Allender, José L. Balcázar, Neil Immerman
• Keywords: Complete Problem, Complexity Classes, Rst-order Isomorphism, STACS 1993, Theoretical Computer Science