Restrictive Acceptance Suffices for Equivalence Problems

Bernd Borchert, Lane A. Hemaspaandra, Jörg Rothe

Abstract: One way of suggesting that an NP problem may not be NP-complete is to show that it is in the class UP. We suggest an analogous new approach—weaker in strength of evidence but more broadly applicable—to suggesting that concrete NP problems are not NP-complete. In particular we introduce the class EP, the subclass of NP consisting of those languages accepted by NP machines that when they accept always have a number of accepting paths that is a power of two. Since if any NP-complete set is in EP then all NP sets are in EP, it follows—with whatever degree of strength one believes that EP differs from NP—that membership in EP can be viewed as evidence that a problem is not NP-complete.