Restrictive acceptance suffices for equivalence problems

Abstract: One way of suggesting that an NP problem may not be NP-complete is to show that it is in the promise class UP. We propose an analogous new method---weaker in strength of evidence but more broadly applicable---for suggesting that concrete NP problems are not NP-complete. In particular, we introduce the promise 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. We show that FewP, bounded ambiguity polynomial time (which contains UP), is contained in EP. The class EP applies as an upper bound to some concrete problems to which previous approaches have never been successful, for example the negation equivalence problem for OBDDs (ordered binary decision diagrams).