Powers-of-Two Acceptance Suffices for Equivalence and Bounded Ambiguity Problems

We study 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 the negation equivalence problem for OBDDs (ordered binary decision diagrams) and the interchange equivalence problem for 2-dags are in EP. We also show that for boolean negation the equivalence problem is in EP^{NP}, thus tightening the existing NP^{NP} upper bound. We show that FewP, bounded ambiguity polynomial time, is contained in EP, a result that seems incomparable with the previous SPP upper bound. Finally, we show that EP can be viewed as the promise-class analog of C_=P.