The Complexity of Decision Versus Search

  • Authors:
  • Mihir Bellare;Shafi Goldwasser

  • Affiliations:
  • -;-

  • Venue:
  • SIAM Journal on Computing
  • Year:
  • 1994

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Abstract

A basic question about NP is whether or not search reduces in polynomial time to decision. This paper indicates that the answer is negative: Under a complexity assumption (that deterministic and nondeterministic double-exponential time are unequal) a language in NP for which search does not reduce to decision is constructed. These ideas extend in a natural way to interactive proofs and program checking. Under similar assumptions, the authors present languages in NP for which it is harder to prove membership interactively than it is to decide this membership, and languages in NP that are not checkable.