Reductions that lie

@article{Adleman1979ReductionsTL,
  title={Reductions that lie},
  author={Leonard M. Adleman and Kenneth L. Manders},
  journal={20th Annual Symposium on Foundations of Computer Science (sfcs 1979)},
  year={1979},
  pages={397-410}
}
All of the reductions currently used in complexity theory (≤p, ≤γ, ≤R) have the property that they are honest. If A ≤ B then whatever machine M reduces A to B is such that: if on input x, M outputs y then x ε A ↔ y ε B. It would appear that this membership preserving property is intrinsic to the notion of reduction. We will see that it is not. We introduce… CONTINUE READING