The Complexity of Decision Versus Search

Mihir Bellare, Shafi Goldwasser
1994 SIAM journal on computing (Print)  
A basic question about NP is whether or not search reduces in polynomial time to decision. We indicate that the answer is negative: under a complexity assumption that deterministic and non-deterministic double-exponential time are unequal we construct a language in NP for which search does not reduce to decision. These ideas extend in a natural way to interactive proofs and program checking. Under similar assumptions we present languages in NP for which it is harder to prove membership
more » ... vely than it is to decide this membership, and languages in NP which are not checkable.
doi:10.1137/s0097539792228289 fatcat:5h53wc3gsbeqjaneurwasrqa5a